The number of five digit numbers that are divisible by 6 which can be formed by choosing digits from 0,1,2,3,4,5 , when repetition is allowed, is

Step-by-step solution

If number is divisible by 6 , then it should be an even number and divisible by 3 also, so sum of the digits should be divisible by 3 . Now last digit can be fill by 0 or 2 or 4 . First place can be filled by 5 choices (except 0 ) second and third can be filled by 6 choices. Now fourth place is filled such that it must be of form 3 k or 3 k+1 or 3 k+2 . So it can be fill by 2 choices ( 0 or 3 ) as whole number must be divisible by 3 so, total numbers aligned & =5 6 6 2 3 & =1080 aligned Hence, option (d) is correct