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

Options

A. 2
B. 3
C. 4
D. none of these

Answer

C

Explanation

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.