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share 5 donuts--Probability

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share 5 donuts--Probability

by nh8404052006 » Sat May 02, 2009 4:08 am
Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?

Please explain, thank
OA: 21
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by deepoe » Sat May 02, 2009 5:00 am
5,0,0
0,5,0
0,0,5

1,1,3
1,3,1
3,1,1

1,2,2
2,1,2
2,2,1

3,2,0
2,3,0
0,3,2
0,2,3
3,0,2
2,0,3

0,1,4
0,4,1
4,1,0
1,4,0
4,0,1
1,0,4


21 :D
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by dumb.doofus » Sat May 02, 2009 2:04 pm
There's another way of doing this without writing all the answer options..

Just write the different ways you can distribute 5 donuts..

a. 1, 2, 2 can be arranged in 3!/2! ways
b. 3, 2, 0 can be arranged in 3! ways
c. 4, 1, 0 can be arranged in 3! ways
d. 5, 0, 0 can be arranged in 3!/2! ways
e. 1, 1, 3 can be arranged in 3!/2! ways

Since we have to distibute donuts.. 0, 0, 0 is not an option, although 0 is a whole number.

Total ways = a + b + c + d + e = 21
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by Brent@GMATPrepNow » Sat May 02, 2009 2:08 pm
There is a quick way to look at this question such that the answer is 7C2.
Can anyone out there see how the question can be tackled such that the answer is 7C2?
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by Brent@GMATPrepNow » Sat May 02, 2009 2:26 pm
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by dmateer25 » Sat May 02, 2009 2:28 pm
Brent,

Isn't this similar to one of the problems you created?? I remember you created one and there was a trick to it, but I don't quite remember what it was.
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by dmateer25 » Sat May 02, 2009 2:29 pm
Brent Hanneson wrote:Image
There it is!! I knew it was something like that but couldn't quite remember!
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by Brent@GMATPrepNow » Sat May 02, 2009 2:41 pm
dmateer25 wrote:Brent,

Isn't this similar to one of the problems you created?? I remember you created one and there was a trick to it, but I don't quite remember what it was.
Nice memory, dmateer25
The original question is at: https://www.beatthegmat.com/very-tricky- ... 25349.html
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by dumb.doofus » Sat May 02, 2009 2:47 pm
Brent Hanneson wrote:Image
Damn cool man!! Nice approach.. I liked it a lot.. super..
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