Answer :
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