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

# A Five Digit Number Divisible By 3 Is To Be Formed Using The Numerals 0, 1, 2, 3, 4 And 5 Without Repetition. The Total Number Of Ways In Which This Can Be Done Is

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## Question

### Solution

Correct option is

216

The sum of the numerals 0, 1, 2, 3, 4 and 5 is 15. We know that five digit is divisible by 3 if and only if the sum of its digits is divisible by 3. Therefore, we should not eight 0 or 3 while forming the five digit numbers. If we do not user 0, then the remaining digit can be arranged in  ways. If we do not use 3, then the remaining digit can be

ways to obtain a five digit number. Thus, the total number of such 5 digit numbers is 120 + 96 = 216.

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