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

Step-by-step solution

Since, a five digit number is formed by using digits 0,1,2,3,4 and 5 , divisible by 3 i.e., only possible when sum of digits is multiple of three which gives two cases. Case I Using digits 0,1,2,4,5 the number of ways =4 4 3 2 1=96 . Case II Using digits 1, 2, 3, 4, 5 the number of ways =5 4 3 2 1=120 Total numbers formed =120+96=216