There are y different travelers who each have a choice of vacationing at one of n different destinations.

[BTGmoderatorDC]

There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?

A. 1/n!
B. n/n!
C. 1/n^y
D. 1/n^(y-1)
E. n/y^n


OA D

Source: Manhattan Prep

[regor60]

Assume some easy numbers and test the answers.

Set Y=3 and n=2

So 3 travelers each have 2 choices. This equals 2^3=8 ways they can be allocated.

Since there are only 2 ways all 3 of them can stay at the same spot, the probability is

2/8 = 1/4

Which of the answers gives 1/4 when the substitution is made ?

Let's try D
1/(2^(3-1)) = 1/2^2 = 1/4. Success.