# How many 5 - digit numbers can be formed from the integers 1, 2, 3, 4, 5, 6, 7, 8, 9, in which at at least one number appears more than once

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by chokeh

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by chokeh

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The number of 5 digit numbers with no restrictions: 9*9*9*9*9 = 9^5 = 59,049

because each digit can be any one of the 9 available digits.

the number of 5 digit numbers with no repetition of any digit:

= 9 * 8 * 7 * 6 * 5 = P(9,5) = permutations of choosing 5 digits out of 9

= 15,120

The number of 5 digit numbers with at least one digit repeating : 59,049 - 15,120

= 43939

because each digit can be any one of the 9 available digits.

the number of 5 digit numbers with no repetition of any digit:

= 9 * 8 * 7 * 6 * 5 = P(9,5) = permutations of choosing 5 digits out of 9

= 15,120

The number of 5 digit numbers with at least one digit repeating : 59,049 - 15,120

= 43939