Question

The Set $A$ has $4$ elements and the Set $B$ has $5$ elements then the number of injective mappings that can be defined from $A$ to $B$ is

• A. $144$
• B. $72$
• C. $60$
• D. $120$

Answer 1

The correct option is D $120$

Let $f$ be such a function. Now, $f$ takes inputs from set $A$ whereas the output value of $f$ comes from set $B$.

Using the fact that injective functions are one-one and onto, $f\left(1\right)$ can take $5$ values, $f\left(2\right)$ can then take only $4$ values ,$f\left(3\right)$ can take only $3$ and $f\left(4\right)$ only $2$. Hence the total number of

functions are $5\times 4\times 3\times 2=120$.