Question

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injections that can be defined from $A$ to $B$ is:

• A. $144$
• B. $12$
• C. $24$
• D. $64$

Answer 1

The correct option is C

$24$

Finding the number of interjections defined from $A$ to $B$:

Given, set $A$ has $3$ elements

Set $B$ has $4$ elements

Injection is also referred as permutation, which shows several conceivable orders or arrangements for a group or number of things.

The formula used will be $P(n,r)=\frac{n!}{(n-r)!}$

Number of injections that can be defined from $A$ to $B$:

$$\begin{gathered} {=}^4{P}_3 \\ =\frac{4!}{[4–3]!} \\ =4\times 3\times 2 \\ =24 \end{gathered}$$

Therefore, the correct answer is option (C).