Question

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

• A. 505
• B. $4^5-5$ !
• C. 600
• D. None of the above

Answer 1

Answer: (A)

Total number of 4-digit numbers $=5\times 5\times 5\times 5$
$=625$
(as each place can be filled by anyone of the numbers 1, 2 , 3,4 and 5)
Numbers in which no two digits are identical $=5\times 4\times 3\times 2$ (i.e., repetition not allowed) $=120$ (as 1 st place can be filled in 5 different ways, 2nd place can be filled in 4 different ways and so on)
Number of 4-digits numbers in which atleast 2 digits are identical
$=625-120$
$=505$