Question : 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
(A) 2
(B) 3
(C) 4
(D) none of these
Answer : option (C)
Solution :
The total number of mapping is n^{n}. The number of one-one mapping is nc_{1} n-1C_{1}…1c_{1}=n!, hence the probability is
\dfrac{n!}{n^{n}}=\dfrac{3}{32}=\dfrac{4!}{4^{4}}Comparing we get, n=4.