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Question

A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer

nC11pnC22p+nC33p....+(1)n1 nCnnp is equal to,


A

(1)n1n!,if P<n

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B

0, if P=n

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C

n!,if P=n

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D

(1)n1n!,if P<n

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Solution

The correct option is D

(1)n1n!,if P<n


F(n,P)=npnC1(n1)p+nC2(n2)p+....(1)n1 nCn11pnpF(4,6)=464C136+4C2264C31646=195512
Also if P < n then probability is zero and if P=n then,nnnC1(n1)n+....+(1)n1 nCn1nnn=n!nn


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