Question

In the decimal system of numeration the number of 6-digit numbers in which the sum of the digits is divisible by 5 is –

• A. 180000
• B. 540000
• C. 5 × 10⁵
• D. None of these

Answer 1

Answer: (A)

180000

Answer 2

× × × × × ×

Sol. Ways : 9 10 10 10 10 6

0 cannot go in the first place. In other four places any digit can go. After filling the first five places, the last place can be filled by 0 or 5, 1 or 6, 2 or 7, 3 or 8, 4 or 9 depending upon whether the sum of five digits filled is of the form 5m, 5m, + 4, 5m + 3, 5m + 2 or 5m + 1 respectively.

\ The required number of numbers = 9 × 10⁴ × 2.