Question

Let $A$ be a set of $4$ elements and $B$ has $3$ elements . From the set of all functions from $A$ to $B$, the probability that it is an onto function is

• A. $\frac{4}{9}$
• B. $0$
• C. $\frac{29}{32}$
• D. $1$

Answer 1

The correct option is A $\frac{4}{9}$

No .of functions from $A$ to $B$ is $3^4=81$ elements

No.of onto functions $4\times 3^2=36$

Probability $\frac{36}{81}=\frac{4}{9}$