Question

How many numbers can be formed using $4$ digits at a time with the digits $1,2,3,4,5,6$. The numbers must contain the digit $4$ and $5$.

Answer 1

Total numbers $=4P_2\times 2P_2$

$=\frac{4!}{2!}\times \frac{2!}{0!}$

$=\frac{4\times 3\times 2!}{2!}\times 2$

$=24$