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Question

Number of ways in which 25 identical things can be distributed among five persons if each gets odd number of things is

A
25C4
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B
12C8
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C
13C3
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D
14C4
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Solution

The correct option is D 14C4
Let person Pi gets xi number of things such that :
x1+x2+x3+x4+x5=25
Let xi=2yi+1 where yi0, then
2(y1+y2+y3+y4+y5)+5=25y1+y2+y3+y4+y5=10

The total number of ways is equal to number of non-negative integral solutions of this equation
=10+51C51=14C4

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