If a five digit number divisible by 3 is to be formed using the numbers 0,1,2,3,4 and 5 without repetition, then the total number of ways this can be done is

Step-by-step solution

Any number is divisible by 3 if sum of its all digit is divisible by 3 . (i) Sum when digits are 0,1,2,3,4=10 not divisible by 3 (ii) Sum when digits are 0,1,2,3,5=11 not divisible by 3 (iii) Sum when digits are 0,1,2,4,5=12 divisible by 3 So, number of 5 digit numbers with 0,1,2,4,5 are 4 4 3 2 1=96 (iv) Sum when digits are 0,1,3,4,5=13 not divisible by 3 (v) Sum when digits are 0,2,3,4,5=14 not divisible by 3 (vi) Sum when digits are 1,2,3,4,5=15 divisible by 3 So, number of 5 digit numbers with 1,2,3,4,5 are 5 4