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In how many ways, 10 identical chocolates be distributed among 3 child
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23 Sep 2021, 09:27
23 Sep 2021, 09:27
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In how many ways, 10 identical chocolates be distributed among 3 children such that each child gets at least 1 chocolate?
A. 36
B. 66
C. 72
D. 78
E. 84.
A. 36
B. 66
C. 72
D. 78
E. 84.
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Joined: 10 Apr 2015
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Re: In how many ways, 10 identical chocolates be distributed among 3 child
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23 Sep 2021, 09:32
23 Sep 2021, 09:32
1
Carcass wrote:
In how many ways, 10 identical chocolates be distributed among 3 children such that each child gets at least 1 chocolate?
A. 36
B. 66
C. 72
D. 78
E. 84.
A. 36
B. 66
C. 72
D. 78
E. 84.
One approach is to look for a pattern
Say the 3 children are A, B, C
We'll denote each outcome as follows: # chocolates for A | # chocolates for B | # chocolates for C
Number of outcomes in which child A receives exactly 1 chocolate
1 | 1 | 8
1 | 2 | 7
1 | 3 | 6
1 | 4 | 5
1 | 5 | 4
1 | 6 | 3
1 | 7 | 2
1 | 8 | 1
8 outcomes
Number of outcomes in which child A receives exactly 2 chocolates
2 | 1 | 7
2 | 2 | 6
2 | 3 | 5
2 | 4 | 4
2 | 5 | 3
2 | 6 | 2
2 | 7 | 1
7 outcomes
Number of outcomes in which child A receives exactly 3 chocolates
3 | 1 | 6
3 | 2 | 5
3 | 3 | 4
3 | 4 | 3
3 | 5 | 2
3 | 6 | 1
6 outcomes
See the pattern?
So, the TOTAL number of outcomes = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= 36
Answer: A
Cheers,
Brent
gmatclubot
Re: In how many ways, 10 identical chocolates be distributed among 3 child [#permalink]
23 Sep 2021, 09:32
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