If 25 blankets are distributed among 5 persons then the probability that each person gets odd number of blankets is
A
14C1029C4
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B
17C429C4
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C
12
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D
10C429C4
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Solution
The correct option is A14C1029C4 Number of blankets each person should get is odd so each person can get 2λi+1 blankets where λi≥0
For 5 persons ⇒2(λ1+λ2+λ3+λ4+λ5)+5=25 ⇒λ1+λ2+λ3+λ4+λ5=10
Number of ways of distributing odd number of blankets will be ⇒10+5−1C5−1=14C4=14C10
Total number of ways to distribute the blankets without any restriction ⇒25+5−1C5−1=29C4 ∴Required probability=14C1029C4