Question

If the set $A$ contains $7$ elements and the set $B$ contains $10$ elements; then the no of one one function from $A$ to $B$ is

• A. ${}^{10}{C}_7$
• B. ${}^{10}{C}_7\times 7!$
• C. $7^{10}$
• D. ${10}^7$

Answer 1

The correct option is B ${}^{10}{C}_7\times 7!$

Number of elements in set $A=m=7$

Number of elements in set $B=n=10$

As, the number of one-one functions from $A$ to $B$ with $m$ and $n$ elements ${=}^n{P}_m{=}^n{C}_m\times m!$

So, the number of one-one functions from $A$ to $B$ with $7$ and $10$ elements ${=}^{10}{P}_7{=}^{10}{C}_7\times 7!$