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Question

The number of 5-digits numbers that can be formed using the digits 0, 1, 1, 2, 3 is

Solution
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If repetitions are allowed, the no. of 5 digit numbers

4×5×5×5×5
4×5×5×5×5=2500
(since '0' cannot come in first place)

=2500

No. of 5 digit numbers in which no number is repeated

4×4!2!
(since '1' occurs twice)

=48


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