(a) Total number of 4-digit numbers = 5 x 5 x 5 x 5 = 625 (as each place can be filled by anyone of the numbers 1, 2, 3, 4 and 5) Numbers in which no two digits are identical = 5 x 4 x 3 x 2 = 120 (i.e. repetition not allowed) (as 1st place can be filled in 5 different ways, 2nd place can be filled in 4 different ways and so on) Number of 4-digits numbers in which at least 2 digits are identical = 625 - 120 = 505