Question

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

• A. $4^5-5!$
• B. $5^4-5!$
• C. $4^5-5$
• D. $5^4-5$

Answer 1

The correct option is B $5^4-5!$

The number of numbers when repetition is allowed = $5^4$
The number of numbers when repetition not allowed = 5!
$\therefore$ The required number of numbers =$5^4–5!$