How many four-digit numbers divisible by 6 are possible using only digits 0 ,   1 ,   3 ,   5 ,   7 without repetition?

Step-by-step solution

We have to form four-digit number which is divisible by 6 Four-digit number should be divisible by 2 and 3 Hence, four-digit number will be even as well as sum of digit must be divisible by 3 Hence, possible digit combination is 0 ,   3 ,   5 ,   7 or 0 ,   1 ,   3 ,   5 The number of ways to arrange 0 ,   3 ,   5 ,   7 when the number is even as well as divisible by 3 is 3 ! The number of ways to arrange 0 ,   1 ,   3 ,   5 when the number is even as well