Question

The number of bijection that can be defined from $A=\{1,2,8,9\}$ to $B=\{3,4,5,10\}$ is

• A. $4^4$
• B. $4^2$
• C. $24$
• D. $18$

Answer 1

The correct option is C $24$

There are 4 inputs $\{1,2,8,9\}$ and 4 outputs $\{3,4,5,10\}$. Hence function will be bijective if and only if each output is connected with only one input.
Therefore number of bijective function is $4!=24$