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One mapping is selected at random from all mappings of the set `S={1,2,3,.... n}` into itself. If the probability that the mapping is one-one is 3/32, then the value of `n` is `2` b. `3` c. `4` d. none of these

A

2

B

3

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The total number of mapping is `n^(n)`. The number of one-one mapping is n!. Hence, the probability is
`(n!)/(n^(n))=(3)/(32) = (4!)/(4^(4))`
Comparing, we get n = 4.
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