Question

The number of $4$ digited numbers that can be formed using the digits $1,2,5,6,7$ (without repetition) that are divisible by $25$ is

Answer 1

Number is divisible by $25$ if the number formed by last two digits is divisible by $25$
Now if the repetition is not allowed
Last two digit can be filled in $2$ ways (i.e., $25,75$) remaining $2$ places with $3$ digits in ${}^3{P}_2$ ways.
$\therefore \text{Number of numbers divisible by}25=2\times {}^3{P}_2=12$