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

Step-by-step solution

We know that a five digit number is divisible by 3 , if and only if sum of its digits (=15) is divisible by 3. Therefore, we should not use 0 and 3 in a same number while forming the five digit numbers. Now, i. In case we do not use 0 , the five digit number can be formed (using digits 1,2,3,4,5 ) in ^5 P ₅=120 ways. ii. In case we do not use 3, the five digit number can be formed (using digits 0,1,2,4,5 ) in ^5 P ₅- ^4 P ₄=5!-4!=120-24=96 ways The total number of such 5 digit number =120+96=216