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

[Hint:5 digit numbers can be formed using digits 0, 1, 2, 4, 5 or by using digits 1, 2, 3, 4, 5 since sum of digits in these cases is divisible by 3.]

Answer 1

A. 216

Explanation:

5-digit numbers can be formed using digits 0, 1, 2, 4, 5

4x4x3x2x1=96

5-digit numbers can be formed using digits 1, 2,3, 4, 5=5!

Total number of ways=5! +96

Hence, Option (A) 216 is the correct answer.