First slide

Theorems of probability

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

Moderate

A

2
B

3
C

4
D

None of these

Solution

The total number of mapping is nⁿ. The number of one-one mapping $^{n} {C_{1}}^{n - 1} C_{1} \dots^{1} C_{1} = n!$
Hence, the probability is $\frac{n!}{n^{n}} = \frac{3}{32} = \frac{4!}{4^{4}}$
Comparing, we get n = 4.

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