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^(y1)
E. n/y^n
OA D
Source: Manhattan Prep
There are y different travelers who each have a choice of vacationing at one of n different destinations.
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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^(31)) = 1/2^2 = 1/4. Success.
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^(31)) = 1/2^2 = 1/4. Success.