Question

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

Answer 1

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