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Q.

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

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a

25C4

b

12C8

c

14C10

d

13C3

answer is C.

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Detailed Solution

Let person Pi gets xi number of things such that     x1+x2+x3+x4+x5=25Let xi=2λi+1, where λi≥0. Then      2λ1+λ2+λ3+λ4+λ5+5=25or  λ1+λ2+λ3+λ4+λ5=10We have to simply obtain the number of non-negative integral solutions of this equation, which is equal to 14C4.
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