Question

Let A be a set of $4$ elements. From the set of all functions from A to A, the probability that it is an into function is?

• A. $\frac{3}{32}$
• B. $0$
• C. $\frac{29}{32}$
• D. $1$

Answer 1

The correct option is A $\frac{3}{32}$

Let set A be of n element and from A to A then no of onto element is n! and total function are $n^2$

$P\left(E\right)=\frac{n!}{n}=\frac{4!}{4\times 4\times 4\times 4}$

$=\frac{4\times 3\times 2}{4\times 4\times 4\times }=\frac{3}{32}$