The sum of all possible 3 -digit numbers formed using the digits 1, 2, 3, 4 and 5 , without repetition, such that the numbers are divisible by 3 , is equal to __________

Step-by-step solution

A number is divisible by 3 if the sum of its digits is a multiple of 3 . We need to select 3 digits from 1, 2, 3, 4, 5 such that their sum is a multiple of 3 . The sum of all 5 digits is 15 . To leave a sum that is a multiple of 3 , the 2 unselected digits must sum to a multiple of 3 . The possible pairs of unselected digits are (1, 2), (1, 5), (2, 4) and (4, 5) . Thus, the valid 3 -digit subsets are: 3, 4, 5 (sum = 12 ) 2, 3, 4 (sum = 9 ) 1, 3, 5 (sum = 9 ) 1, 2, 3 (sum = 6 ) For each subset, the sum of all 3 -dig