Question

The sum of the digits in the unit place of all numbers formed with the help of 3, 5, 6, 7, 8 taken all at a time is (repetition of digits are not allowed)

• A. 696
• B. 676
• C. 1296
• D. 1376

Answer 1

Answer: (A)

696

Answer 2

The set of digits is {3, 5, 6, 7, 8}. The sum of these digits is $3 + 5 + 6 + 7 + 8 = 29$. When all $n=5$ digits are used to form numbers without repetition, each digit appears in the unit place $(n-1)! = (5-1)! = 4! = 24$ times. The sum of the digits in the unit place of all such numbers is: Sum = (Sum of digits) $\times$ (n-1)! Sum = $29 \times 24 = 696$.