share 5 donuts--Probability

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nh8404052006: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Wed Aug 27, 2008 9:58 am

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
Source : Gmat-maths.blocked

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Source: Beat The GMAT — Problem Solving | Sat May 02, 2009 4:08 am

deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

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

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dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

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

One love, one blood, one life. You got to do what you should.
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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?

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat May 02, 2009 2:26 pm

Brent Hanneson - Creator of GMATPrepNow.com

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dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

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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dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Sat May 02, 2009 2:29 pm

Brent Hanneson wrote:

There it is!! I knew it was something like that but couldn't quite remember!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

by dumb.doofus » Sat May 02, 2009 2:47 pm

Brent Hanneson wrote:

Damn cool man!! Nice approach.. I liked it a lot.. super..

One love, one blood, one life. You got to do what you should.
https://dreambigdreamhigh.blocked/
https://gmattoughies.blocked/

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