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Q.
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
Permutations and Combinations
Solution:
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
$=625-120$
$=505$