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Anagrams |
WITH FEWER LETTERS
Most of the time, the dictionary contains no 7 letter word for our 7 Scrabble tiles.
Even though we drag them around and exchange them for new letters,
sometimes we do well to make a 3 or 4 letter word from 7 letters.
QUESTIONS
How many 4 letter arrangements can you make from 7 letters?
How many k letter arrangements can you make from 7 letters?
How were the arrangements in the table below counted?
| n | k | Arrangements |
| 7 | 0 | 1 |
| 7 | 1 | 7 |
| 7 | 2 | 42 |
| 7 | 3 | 210 |
| 7 | 4 | 840 |
| 7 | 5 | 2520 |
| 7 | 6 | 5040 |
| 7 | 7 | 5040 |
Can you find a rule for counting k letter arrangements out of n letters?
That is, generalize your rule from 7 to n = any counting number,
and k = any counting number less than or equal to n.
How many k letter arrangements can you make from n letters?
Can you state a rule in English for counting the arrangements of k things taken from n different things?
Can you write a formula for your rule where n is any number of letters,
and k is the number of letters that you select from the n letters?
How is this rule similar to the rule for counting arrangements in the previous assignment?
How are you applying the counting rule from the Counting assignment?
How does this rule differ from the rule for counting arrangements in the previous assignment?
That is, generalize your rule from 7 to n = any counting number,
and k = any counting number less than or equal to n.
How many k letter arrangements can you make from n letters?
Can you state a rule in English for counting the arrangements of k things taken from n different things?
Can you write a formula for your rule where n is any number of letters,
and k is the number of letters that you select from the n letters?
How is this rule similar to the rule for counting arrangements in the previous assignment?
How are you applying the counting rule from the Counting assignment?
How does this rule differ from the rule for counting arrangements in the previous assignment?
- Assume that all n objects are different.
- None of the k objects is repeated.
- Order of the k objects is counted.
ASSIGNMENT
Pick one problem from the list below that no one else has picked.
For 4 points, copy and answer the question in a comment.
Tell us which question you are answering.
Show us how you got your answer by answering the questions above under QUESTIONS.
YOU MAY NOT USE ANY SYMBOLS IN YOUR PROBLEM EXCEPT DIGITS (0-9) AND THE 4 OPERATORS + - * /
DO NOT USE EXPONENT SYMBOLS LIKE ^ . EXPLAIN ALL SOLUTIONS WITH ONLY + - * /
NO FUNNY SYMBOLS FROM FORMULAS YOU COPIED FROM SOMEWHERE ARE ALLOWED.
USE OF SUCH SYMBOLS WILL DELETE YOUR COMMENT.
For 3 points, draw a diagram that pictures your solution. Use the flower applet.
Paste your diagram in a comment.
- Assume that all n objects are different.
- None of the k objects is repeated.
- Order of the k objects is counted.
- HOW MANY WAYS CAN YOU ...
- Pick 1 letter from the alphabet?
- Play 2 songs out of a collection of 52?
- Place 3 X's on a tic-tac-toe grid?
- Choose 4 linebackers from 11 football players for specific positions?
- Deal 5 cards from a 52 card deck?
- Select 6 infielders for 6 positions from 9 baseball players?
- Visit 7 out of 10 cities on your vacation?
- Shop 8 stores out of 10 in the mall?
- Pick 9 players out of 20 for baseball positions?
- Visit 10 state capitals?
- Pick 11 players out of 20 for football positions?
- Eat a dozen donuts from a box of 13?
- Decide which of 13 homes to deliver 3 Looloolo pizzas?
- Pick 3 books to read from a shelf containing 14 books?
- Hire 3 people for 3 jobs from 15 applicants?
- Elect a President, Secretary, and Treasurer from a fraternity with 16 members?
- Count how 3 people can have 3 different birthdays?
- Sing 3 notes from the first 8 notes of "Joy to the World".
- Select 3 outfielders for left, center, and right field from 9 baseball players?
- Pick 3 different digits from the 10 digits: (0 1 2 3 4 5 6 7 8 9)?
- Make 3 letter acronyms if no letter is repeated?
- Seat 3 ladies in 4 chairs?
- Seat 4 ladies in 3 chairs and leave 1 standing?
- Seat 4 ladies in 2 chairs and leave 2 standing?
- Seat 5 ladies in 2 chairs and leave 3 standing?
- Seat 5 ladies in 3 chairs and leave 2 standing?
- Seat 5 ladies in 4 chairs and leave 1 standing?
- Seat 6 ladies in 5 chairs and leave 1 standing?
- Seat 6 ladies in 4 chairs and leave 2 standing?
- THIS ONE IS FOR LATECOMERS TO SEND ME PRIVATELY:
Watch 4 Blockbuster movies out of 30 new ones.
Comments:
From wHolt - 12/12/06 12:16 PM
From GolfGirl - 12/11/06 9:08 PM
#9 Pick 9 players out of 20 for baseball positions.
20*19*18*17*16*15*14*13*12=6.09493248
From BassLady - 12/2/06 8:04 PM
#6 - I don't think anyone has done this problem, or at least I hope not. I saw that mine was taken by someone else.
Select 6 infielders for 6 positions from 9 baseball players.
9 x 8 x 7 x 6 x 5 x 4 = 60,480 different ways to choose the players.
I am working on my flower. I have the stems and colors okay, but my radii is not working well yet. I think I understand the rule of the radii, but not fully understanding how to make it work. 9 is my number and I am working on a way to fit it into the radii.
From wHolt - 12/2/06 12:52 PM
From Cheana - 12/1/06 9:11 PM
#16 Elect a President, Secretary, and Treasurer from a fraternity with 16 members?
16*15*14=1200 Assuming a single person cannot hold more than one office.
N=16 K=3
From Poovey - 11/28/06 7:39 PM
How many ways can you................
8 Shop 8 stores out of 10 in the mall?
N=10, K=8 10x9x8x7x6x5x4x3 = 1,814,400
From wHolt - 11/27/06 9:26 AM
Did you not have 9 stores to choose from at one point in your shopping?
From Poovey - 11/26/06 5:48 PM
How many ways can you................
8 Shop 8 stores out of 10 in the mall?
N=10, K=8 10x9x8x7x6x5x4x3 = 1,814,400
From Melewen - 11/26/06 10:50 AM
From Melewen - 11/20/06 3:20 PM
How many ways can you..
18. Sing 3 notes from the first 8 notes of "Joy to the World".
If you're trying to find 2 ways to arrange n, the formula is n x n-1. If you're trying to find 3 ways to arrange n, the formula is n x n-1 x n-2. If you're trying to find 4 ways, then it's n x n-1 x n-2 x n-3, and so on. Therefore, to find how many ways you can sing 3 notes from the first 8 notes of "Joy to the World," you would say
8 x 7 x 6 = 336
336 ways to sing 3 notes from the first 8 notes of "Joy to the World."
Diagram coming!
From Houdini - 11/20/06 12:29 PM
From wHolt - 11/20/06 10:10 AM
7Iron - thanks for the correction.
Houdini - that's a very fuzzy donut. Blueberry perhaps?
How many ways are there to eat all 13 donuts?
From Houdini - 11/20/06 7:53 AM
Finally something I'm good at... eating donuts!
#12 How many ways can you eat 12 donuts from a box of 13?
n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8)(n-9)(n-10)(n-11)=
13x12x11x10x9x8x7x6x5x4x3x2=6227020800
Number of 4 letter combos out of seven letters: 7(7-1)(7-2)(7-3)=840
3 letter combos:7(7-1)(7-2)(7-3)(7-4)=2520
2 letters:7(7-1)(7-2)(7-3)(7-4)(7-5)=5040
From 7Iron - 11/19/06 8:38 PM
#3 How many ways can you ...Place 3 x's on a tic tac toe board? 504 ways
9*8*7 = 504
1. How many 4 letter arrangements can you make from 7 letters? 840 arrangements
2. 7(7-1)(7-2)....(7-k) / k(k-1)(k-2)......(k-(k+1)
3.
| n | k | arrangements | how? |
| 7 | 0 | 1 | 1 |
| 7 | 1 | 7 | 7 |
| 7 | 2 | 42 | 7*6 |
| 7 | 3 | 210 | 7*6*5 |
| 7 | 4 | 840 | 7*6*5*4 |
| 7 | 5 | 2520 | 7*6*5*4*3 |
| 7 | 6 | 5040 | 7*6*5*4*3*2 |
| 7 | 7 | 5040 | 7*6*5*4*3*2*1 |
From wHolt - 11/18/06 1:42 PM
From wHolt - 11/17/06 2:31 PM
Everyone make sure to read others examples. They are much the same as yours.
Only the numbers have been changed to indict the impatient.
GolfGirl - are you saying that you have 20 ways to choose a player for each position?
How many players do you have after you assign a player to shortstop?
Or can you assign the same player to first base also?
BassLady - how many state capitals are there?
How many ways to visit 10 of them?
Draco - you finished the problem, so I deleted it to give BassLady a chance.
7Iron - there are 9 spaces on a tic-tac-toe board. Fill 3 of them with x's.
How many ways to fill
the first?
the second?
the third?
Bubba - Kathi claimed #22. Study the others. Pick another.
Lexiowen - how is your problem similar to Zonino's above?
Is Zonino's correct?
How many ways to pick the
first donut?
second donut?
third donut?
From Lexiowen - 11/16/06 11:27 PM
Eat a dozen donuts from a box of 13.
im so lost
From Zonino - 11/16/06 8:46 PM
11. Pick 11 players out of 20 for football positions?
The formula to use is n*(n-1)*(n-2)...(n-k+1) or
20*19*18*17*16*15*14*13*12*11*10 or 6,704,425,728,000 ways.
From Bubba - 11/16/06 8:38 PM
number 22
4 ladies 3 sitting 1 standing
or simplified to 4 ladies in 4 different positions
nxn
16 possible positions
From BassLady - 11/16/06 6:43 PM
#10 - Visit 10 state capitals? 3,628,800
10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1
N = 10 K = 10
If there were 11 cities I would change the formula to 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
From wHolt - 11/16/06 11:01 AM
Pac - why did you divide (15*14*13*12*11*10*9*8*7*6*5*4*3*2*1) by (12*11*10*9*8*7*6*5*4*3*2*1)?
Poovey - where is the 10 in your equation?
David - interesting drawing. is that a species of kiwi?
Trixie - thanks for the explanation
JooJoo - where are the 2652 red tips representing the 2652 number of ways?
I only see 104 red tips.
Fro - nice knitting
Centerfield - if yor computer does not like it, try less numbers,
but show us in your data boxes what you did.
From CenterField - 11/15/06 9:49 PM
#5. Deal 5 cards from a 52 card deck?
52*51*50*49*48 = 311,875,200
You have five possible positions, and none of them will be repeated answers. The first position could be any of the 52 cards, the next one could be any except that one, the next one could be any except those two, etc.
(When I attempted to make a flower diagram of this in the applet, my computer threw a fit. I'll try again later.)
From Fro - 11/15/06 8:55 PM
21. Make 3 letter acronyms if no letter is repeated?
N= 26 K=3
26*25*24=15600
From JooJoo - 11/15/06 10:22 AM
2. How many ways can you play 2 songs out of a collection of 52?
There are 2652 ways to play 2 songs out of a collection of 52
I got this answer from:
(52 x 51 x 50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (50 x 49 x 48 x 47 x 46 x 45 x 44 x 43 x 42 x 41 x 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 x 30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)= 2652 ways to play 2 songs from a collection of 52
From Trixie - 11/15/06 1:16 AM
From David - 11/14/06 11:08 PM
17. Count how 3 people can have 3 different birthdays?
a sane person would just write it as 365*364*363=48228180 possibilities
but Ill write it as
(365*364*363*362*361*360*359*358*357*356*355*354*353*352*351*350*349*348*347*34
6*345*344*343*342*341*340*339*338*337*336*335*334*333*332*331*330*329*328*327*
326*325*324*323*322*321*320*319*318*317*316*315*314*313*312*311*310*309*308*307
*306*305*304*303*302*301*300*299*298*297*296*295*294*293*292*291*290*289*288*2
87*286*285*284*283*282*281*280*279*278*277*276*275*274*273*272*271*270*269*268*
267*266*265*264*263*262*261*260*259*258*257*256*255*254*253*252*251*250*249*24
8*247*246*245*244*243*242*241*240*239*238*237*236*235*234*233*232*231*230*229*2
28*227*226*225*224*223*222*221*220*219*218*217*216*215*214*213*212*211*210*209
*208*207*206*205*204*203*202*201*200*199*198*197*196*195*194*193*192*191*190*18
9*188*187*186*185*184*183*182*181*180*179*178*177*176*175*174*173*172*171*170*
169*168*167*166*165*164*163*162*161*160*159*158*157*156*155*154*153*152*151*150
*149*148*147*146*145*144*143*142*141*140*139*138*137*136*135*134*133*132*131*1
30*129*128*127*126*125*124*123*122*121*120*119*118*117*116*115*114*113*112*111*
110*109*108*107*106*105*104*103*102*101*100*99*98*97*96*95*94*93*92*91*90*89*8
8*87*86*85*84*83*82*81*80*79*78*77*76*75*74*73*72*71*70*69*68*67*66*65*64*63*62
*61*60*59*58*57*56*55*54*53*52*51*50*49*48*47*46*45*44*43*42*41*40*39*38*37*36
*35*34*33*32*31*30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*
9*8*7*6*5*4*3*2*1)/(362*361*360*359*358*357*356*355*354*353*352*351*350*349*348*347*346*345*344*343
*342*341*340*339*338*337*336*335*334*333*332*331*330*329*328*327*326*325*324*323
*322*321*320*319*318*317*316*315*314*313*312*311*310*309*308*307*306*305*304*303
*302*301*300*299*298*297*296*295*294*293*292*291*290*289*288*287*286*285*284*28
3*282*281*280*279*278*277*276*25*274*273*272*271*270*269*268*267*266*265*264*263
*262*261*260*259*258*257*256*255*254*253*252*251*250*249*248*247*246*245*244*243
*242*241*240*239*238*237*236*235*234*233*232*231*230*229*228*227*226*225*224*223
*222*221*220*219*218*217*216*215*214*213*212*211*210*209*208*207*206*205*204*203
*202*201*200*199*198*197*196*195*194*193*192*191*190*189*188*187*186*185*184*183
*182*181*180*179*178*177*176*175*174*173*172*171*170*169*168*167*166*165*164*163
*162*161*160*159*158*157*156*155*154*153*152*151*150*149*148*147*146*145*144*143
*142*141*140*139*138*137*136*135*134*133*132*131*130*129*128*127*126*125*124*123
*122*121*120*119*118*117*116*115*114*113*112*111*110*109*108*107*106*105*104*103
*102*101*100*99*98*97*96*95*94*93*92*91*90*89*88*87*86*85*84*83*82*81*80*79*78*
77*76*75*74*73*72*71*70*69*68*67*66*65*64*63*62*61*60*59*58*57*56*55*54*53*52*5
1*50*49*48*47*46*45*44*43*42*41*40*39*38*37*36*35*34*33*32*31*30*29*28*27*26*25
*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)=48228180 possibilities
In english, it means that the first persons birthday could be any of the 365 possible days of the year. The second persons birthday could be any of the 365 possible minus the first persons birthdate, so 364 possibilities there. Finally, the third persons birthday can only be one of the remaining 363 possible dates since person one and person two already have dibs on their respective birthdays.
wanna see a computer slowing, mind numbing flower? I thought so....
I have way too much time on my hands
From Poovey - 11/14/06 6:27 PM
#8 Shop 8 stores out of 10 in the mall?
8x7x6x5x4x3x2x1= 40,320 ways ?????????????
From Pac - 11/14/06 3:37 PM
Revised from my comment above!
#15: Hire 3 people for 3 jobs from 15 applicants...
n=15, k=3
(15*14*13*12*11*10*9*8*7*6*5*4*3*2*1) / (12*11*10*9*8*7*6*5*4*3*2*1) = 2730 options for hiring
From wHolt - 11/14/06 12:37 PM
DirtyBird - the table for scrabble tiles does not fit your problem.
Trixie - does your method deliver 3 pizzas or 4 pizzas: N (N-1) * (N-2) * (N-3)?
From Trixie - 11/14/06 1:04 AM
#13 Decide which of 13 homes to deliver 3 Looloolo pizzas?
N (N-1) * (N-2) * (N-3)
N=13 K= 3
13*12*11 = 1716
From Tiger - 11/13/06 9:32 PM
#20 Pick 3 numbers from 10 numbers. 10*9*8=720
From DirtyBird - 11/13/06 7:54 PM
4) Choose 4 linebackers from 11 football players for specific positions?
11*10*9*8=7920 positions
N=11 K=4
N(N-1)*(N-2)*(N-3)
How were the arrangements in the table below counted?
| n | k | Arrangements |
| 7 | 0 | 1 |
| 7 | 1 | 7 (7*1=7) |
| 7 | 2 | 42 (7*6=42) |
| 7 | 3 | 210 (7*6*5=210) |
| 7 | 4 | 840 (7*6*5*4=840) |
| 7 | 5 | 2520 (7*6*5*4*3=2520) |
| 7 | 6 | 5040 (7*6*5*4*3*2=5040) |
| 7 | 7 | 5040 (7*6*5*4*3*2*1=5040) |
From wHolt - 11/13/06 10:59 AM
How many shops does your equation actually indicate you shopped at?
From Poovey - 11/12/06 7:34 PM
#8 Shop 8 stores out of 10 in the mall?
10x9x8x7x6x5x4x3x2x1= 3,628,800 ways
From wHolt - 11/11/06 12:16 PM
yet your method indicates that you only have 8.
Can you justify your calculation?
From Poovey - 11/11/06 8:57 AM
#8 Shop 8 stores out of 10 in the mall?
8x10x10x10x10x10x10x10x10x10= 8,000,000,000 ways
From SuperDuke - 11/9/06 1:46 PM
#14 How many ways can you pick three books from a shelf of fourteen?
14 books - minus 1 book - thirteen books - minus 1 book - 12 books left to choose from.
14*13*12 = 2184 possible ways
N=14, K=3
N*(N-1)*(N-2) K is equal to the total number of descending integers from N. These descending integers make the factorial product which is your possibilities (answer).
Example: possible combinations of four letters from eight [N=7 K=4] = [ N*(N-1)*(N-2)*(N-3) ] = [7*6*5*4= 840]
From wHolt - 11/9/06 1:15 PM
and once again you only illustrated 10, 9, and 8
From Harkar - 11/8/06 7:49 PM
n=10
k=7
10 cities – -1 city – 9 cities – -1 city – 8 cities – -1 city = 7 cities remain to choose from.
Answer: 10*9*8*7*6*5*4 = 604,800
There are 604,800 ways to visit 7 out of 10 cities on my vacation.
Formula: n * (n-1) * (n-2) * (n-3) … where k = # of descending numbers from n
Example:
For n = 7, k=3 -> 7*6*5
From wHolt - 11/8/06 11:22 AM
Pac -
how many ways may you choose to fill the first job?
how many for the 2nd?
how many for the 3rd?
Poovey -
how many shops may you choose from for your first visit?
how many for the 2nd?
how many for the 3rd?
how many for the 4th?
how many for the 5th?
how many for the 6th?
how many for the 7th?
how many for the 8th?
Kathi-
how many chairs may you choose from for the first lady?
how many for the 2nd?
how many for the 3rd?
do you have 4 ladies?
From Kathi - 11/8/06 10:47 AM
# 22
How many ways can you sit 3 ladies in 4 chairs?
4 chairs, 4 objects (3 ladies and one empty chair) = 24 choices
4*3*2*1 = 24 ways to seat the ladies
You take the 4 objects (3 ladies and one empty chair) n and multiply it by n-k.
4(4-3)(4-2)(4-2) to equal the number of different outcomes you could have for each seating arrangment.
n(n-1)(n-2)(n-3)...to k.
From Poovey - 11/7/06 5:38 PM
#8 Shop 8 stores out of 10 in the mall?
8x10x10x10x10x10x10x10x10x10= 8,000,000,000 ways
I am working on my flower now...............
From Pac - 11/6/06 4:17 PM
The questions...
The arrangements in the table were counted like this:
For n=7, k=0... (7*6*5*4*3*2*1) / (7*6*5*4*3*2*1) = 1 arrangement
For n=7, k=4... (7*6*5*4*3*2*1) / (3*2*1) = 840 arrangements
For n=7, k=x... (7*6*5*4*3*2*1) / ( (n-k)*(n-k-1)*(n-k-2) ) until n-k-?=1
So for n=15, k=10... (15*14*13*12*11*10*9*8*7*6*5*4*3*2*1) / (5*4*3*2*1) = 360,360 arrangements
#15. Hire 3 people for 3 jobs from 15 applicants?
n=15, k=3
(15*14*13*12*11*10*9*8*7*6*5*4*3*2*1) / (12*11*10*9*8*7*6*5*4*3*2*1) = 2730 options for hiring
From wHolt - 11/6/06 1:50 PM
From Kathi - 11/6/06 8:30 AM
# 22
How many ways can you sit 3 ladies in 4 chairs?
4 chairs, 4 objects (3 ladies and one empty chair) = 24 choices
4*3*2*1 = 24 ways to seat the ladies
n(n-1)(n-2)...
From Boki - 11/4/06 5:15 PM
From Boki - 11/4/06 5:06 PM
1. The number of total 4 letter arrangements from 7 letters is:
(7*6*5*4*3*2*1)=7*6*5*4 = 840
2. These are ordered arrangements where we have to arrange the elements of a set from the first one to the last one. If we have to take (at the time) k elements from n distinct objects, we will do it by using this formula for permutation (which is a counting rule for the arrangements of elements in a distinct order):
If n=7 different letters taken r=4 at a time, there are 7 ways to choose the first letter, 6 ways to choose the second letter, and 5 ways to choose the third letter, and 4 ways to choose fourth letter.
7(7-1)(7-2)(7-3)(7-4+1)=7*6*5*4 =840
3. The arrangements in the table are counted by using same formula for permutations.
In general, the formula for counting k objects (where none is repeated) arrangements
out of n different objects will be:
n(n − 1)(n − 2)· · · to k factors
or
n(n-1)(n-2)(n-3)…….. (n-k+1)
This assignment is similar to counting assignment, but different in total number of arrangements.
Here the total number of arrangements is smaller than in previous assignment.
HOW MANY WAYS CAN YOU ...
- Pick 1 letter from the alphabet?
n=26
k=1
26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1/25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1= 26
There are 26 choices to pick 1 letter from the alphabet.
From wHolt - 11/4/06 2:15 PM
From Boki - 11/3/06 2:39 PM
Answers to the questions:
1. The number of total 4 letter arrangements from 7 letters is:
(7*6*5*4*3*2*1)/(3*3*1)=7*6*5*4 = 840
2. These are ordered arrangements where we have to arrange the elements of a set from the first one to the last one. If we have to take (at the time) k elements from n distinct objects, we will do it by using this formula for permutation (which is a counting rule for the arrangements of elements in a distinct order):7(7-1)(7-2)(7-3)(7-4+1)=7*6*5*4 =840
3. The arrangements in the table are counted by using same formula for permutations.
In general, the formula for counting k objects (where none is repeated) arrangements
out of n different objects will be:
n(n-1)(n-2)(n-3)…….. (n-k+1)
This assignment is similar to counting assignment, but different in total number of arrangements.
Here the total number of arrangements is smaller than in previous assignment.
HOW MANY WAYS CAN YOU ...
- Pick 1 letter from the alphabet?
we have:
n=26
k=1
26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1/25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1= 26
There are 26 choices to pick 1 letter from the alphabet.
From wHolt - 11/3/06 12:09 PM
From wHolt - 11/2/06 11:30 AM
| # | Alias | Date Started |
| 1 | Boki | 11/03 |
| 2 | JooJoo | 11/15 |
| 3 | 7Iron | 11/10 |
| 4 | DirtyBird | 11/14 |
| 5 | Centerfiled | 11/16 |
| 6 | BassLady | 12/03 |
| 7 | Harkar | 11/09 |
| 8 | Poovey | 11/08 |
| 9 | GolfGirl | 11/17 |
| 10 | BassLady Draco | 11/17 |
| 11 | Zonino | 11/17 |
| 12 | Houdini | 11/20 |
| 13 | Trixie | 11/14 |
| 14 | SuperDuke | 11/10 |
| 15 | Pac | 11/07 |
| 16 | Cheana | 12/02 |
| 17 | David | 11/15 |
| 18 | ||
| 19 | ||
| 20 | Tiger | 11/14 |
| 21 | Fro | 11/16 |
| 22 | Kathi | 11/06 |
| 23 | ||
| 24 | ||
| 25 | ||
| 26 | ||
| 27 | ||
| 28 | ||
| 29 | ||
| 30 | ||
| 31 |
Last Modified 11/7/06 12:42 PM
now tell us what the humongous number is
and how you found it.