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22 May 2019, 16:01
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
34% (01:36) correct
66%
(01:20)
wrong
based on 296
sessions
History
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Not Attempted Yet
In how many ways can 5 apples (identical) be distributed among 4 identical baskets?
A) 6
B) 20
C) 51
D) 56
E) 4^5
A) 6
B) 20
C) 51
D) 56
E) 4^5
22 May 2019, 16:02
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dabaobao
Official Solution
Credit: Veritas Prep
As we have seen previously, 5 fruits can be split into 4 groups in the following ways: {5, 0, 0, 0}, {4, 1, 0, 0}, {3, 2, 0, 0}, {3, 1, 1, 0}, {2, 2, 1, 0}, {2, 1, 1, 1}
Here, {5, 0, 0, 0} means that one basket has all 5 apples and the rest of the baskets are empty. Since the baskets are all identical, there is only 1 way of doing this.
{4, 1, 0, 0} means that one basket has 4 apples, another one has 1 apple and the rest of the baskets are empty. Since the fruits and the baskets are all identical, there is again only 1 way of doing this.
You have to select neither the fruits nor the baskets since they are all identical. You only have to decide how to distribute the apples in 4 groups. Therefore, each one of these cases will give us only one different way of distributing the fruits. Since there are 6 such cases, there are only 6 different ways of distributing the fruits.
ANSWER: A
dabaobao
Total partitions = 6
5000
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3200
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2111
2210
Ans (A)
