Question

If $n\left(A\right)=4$ and $n\left(B\right)=6$. then, the number of one-one function from $A$ to $B$ is.

• A. $24$
• B. $60$
• C. $120$
• D. $360$

Answer 1

The correct option is D

$360$

Explanation of the correct option.

Given: $n\left(A\right)=4$ and $n\left(B\right)=6$.

Since $n\left(B\right)>n\left(A\right)$ and the function is one-one function.

Thus, the number of one-one functions mapping from $A$ to $B$ is

$\begin{array}{rcl}{}^{n\left(B\right)}P_{n\left(A\right)}& =& {}^{6}P_4\\ & =& \frac{6!}{(6-4)!}\left[\because {}^{n}P_r=\frac{n!}{\left(n-r\right)!}\right]\\ & =& \frac{6\times 5\times 4\times 3\times 2!}{2!}\\ & =& 360\end{array}$

Hence, option(D) i.e. $360$ is the correct option.