Question

A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

• A. 216
• B. 600
• C. 240
• D. 3125

Answer 1

The correct option is A

216

A number is divisible by 3 when the sum of the digits of the number is divisible by 3.

Out of the given 6 digits, there are only two groups consisting of 5 digits whose sum is divisible by 3.

1 +2+3 + 4 + 5 = 15

0+ 1 + 2 + 4 + 5 = 12

Using the digits 1, 2, 3, 4 and 5, and 5 digit numbers that can be formed = 5!

Similarly, using the digits 0, 1, 2, 4 and 5, the number that can be formed = 5! - 4! (since the first digit cannot be 0)

$\therefore$ Total numbers that are possible 5! + 5! - 4! = 240 - 24 = 216