The number of four digit numbers that can be formed with the digits $1,2,3,4$ and $5$ in which atleast two digits are identical is

The correct option is D. $5^4-5!$
The number of four digit numbers formed by the digits $1,2,3,4$ and $5$ , when repetition is allowed = $5^4$
The number of numbers when repetition not allowed $=5!$
$\therefore$ The required number of numbers $=5^4–5!$