Question

The total number of injections (one-one into mappings) from $\left\{a_1,a_2,a_3,a_4\right\}$ to $\left\{b_1,b_2,b_3,b_4,b_5,b_6,b_7\right\}$ is

• A. $400$
• B. $420$
• C. $800$
• D. $840$

Answer 1

The correct option is D

$840$

One one into mappings:

Given : $A=\left\{a_1,a_2,a_3,a_4\right\}$ and $B=\left\{b_1,b_2,b_3,b_4,b_5,b_6,b_7\right\}$

$n\left(A\right)=4$ and $n\left(B\right)=7$

Therefore, total number of injections$={}^{7}P_4$

$$\begin{gathered} =\frac{7!}{3!} \\ =\frac{7\times 6\times 5\times 4\times 3!}{3!} \\ =840 \end{gathered}$$

Hence option (D) is the correct option.