Question

One mapping is selected at randon from all mappings of the set $S=\{1,2,3,.....,n\}$ into itself. If the probability that mapping is one-one is $3/32$ then the value of $n$ is

• A. $2$
• B. $3$
• C. $4$
• D. None of these

Answer 1

The correct option is C $4$

Total number of possible mapping $=n\times n\times n.....n$ $n$times

$=n^n$ times

Favorable cases $:n\times (n-1)(n-2)....$

Favorable cases are are found by removing the possibility mapping of the number by which other number is mapped initially.

So, $P=\frac{n!}{n^n}$

$=\frac{3\times 8}{16\times 2\times 8}$

$\Rightarrow$ $n=4.$

Hence, the answer is $4.$