First slide

Permutations

Question

A five 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, this can be done is

Moderate

A

240
B

3125
C

600
D

216

Solution

As $0 + 1 + 2 + 3 + 4 + 5 = 15$ , for a five digit number to be divisible by 3 either do not use 0 or 3.
When 0 is not used, the number of such numbers is 5! and when 3 is not used,
the number of such numbers is $5! - 4!$
$∴$ Required number of ways $= 5! + (5! - 4!) = 216$

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