The number of four digited numbers formed by 1, 2, 5, 6, 7 divisible by 25 is

Given digits are 1, 2, 5, 6, 7

A number is divisible by 25 when last 2 digits of the number is divisible by 25.

Last 2 boxes can be filled by 25, 75 in 2 ways

Remaining 2 boxes can be filled by remaining 3 digits in ${}^3{P}_2$  ways.

$\therefore$  Required 4 digit numbers ${=}^3{P}_2\times 2$

       $=12$