Question

If repetition is allowed, then the total number of $4$ digit numbers that can be formed using the digits $1,2,5,6,7$ and that are divisible by $4$, is

Answer 1

For all possible $4$ digit number repetition is allowed
Last two digit can be filled in $6$ ways $[\text{i.e}12,16,52,56,72,76]$ remaining $2$ places can be filled with $5$ digits in $5\times 5=25$ ways.
$\therefore \text{Number of numbers divisible by}4=6\times 25=150$