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`

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.