Question

If $A=\{1,3,5,7\}$ and $B=\{1,2,3,4,5,6,7,8\}$, then the number of one-one functions from $A$ into $B$is

Answer 1

The number of one-one function from $A$ into $B$ is:

Given

$$\begin{gathered} A=\{1,3,5,7\} \\ B=\{1,2,3,4,5,6,7,8\} \\ n\left(A\right)=4 \\ n\left(B\right)=8 \end{gathered}$$

The number of one-one function from $A$ into $B$ is given by

$$\begin{gathered} =n\left(B\right)p_{n\left(A\right)} \\ =8p_4 \\ =8\times 7\times 6\times 5 \\ =1680 \end{gathered}$$

Hence, the number of one-one function from $A$ into $B$ is $\mathbf{1680}$.