Question

A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is
(a) 216
(b) 600
(c) 240
(d) 3125

Answer 1

Five digit number is to be formed from 0,1,2,3,4 and 5.
Such that number is divisible by 3.
Any number is divisible by 3 if sum of its digits out of these digits,
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5 sum up to be a multiple of 3
→ for 1,2,3,4,5,
The number of ways a five digit number which is divisible by 3 is 5 × 4 × 3 × 2 × 1 (∵ no restriction is there)
→ for 0,1, 2, 4, 5
The number of ways a five digit number which is divisible by 3 is 4 × 4 × 3 × 2 × 1 = 96 (∵ 0 cannot be placed or first place)
∴ Total number formed
= 120 + 96
= 216
Hence, the correct answer is option A.