# math

Given a four digit number XXXX, are there more permutations if repetition is allowed or not allowed?

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1. with no repetitions, there are only 4! permutations.
With repetition, there are 10^4 (or maybe 9*10^3 if you disallow leading zeros) choices.

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2. if a zero is allowed in the lead position, then with no repetition, there would be
10(9)(8)(7) ways
if a zero is allowed in the lead position, and repetition is allowed, there would be
10^4 ways

If zero is not allowed, with no repetition: 9(9)(8)(7)
zero not allowed, but with repetition: 9(10^3)

If XXXX is a specified number, and the numbers are all different,
then 4! , as Steve said in his first answer

If XXXX is a specified number and some of the numbers are duplicates, then more
information is needed.

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