How many 5 digit numbers that are divisible by 4 can be formed using the digits from 0 to 6 if no digit is to occur more than once in each number?

Answer 1

There are 7 digits from 0-6

To determine if a number is divisible by 4, we only need look at the last 2 digits. Possibilities are:

[135][26] => 12, 16, 32, 36, 52, 56

and

[0246][04] => 04, 20, 24, 40, 60, 64 (ignoring 00 and 44)

There are 8 combinations without a 0, and 4 with a 0.

Of the 8 combinations without a 0, We can only pick 4 of the remaining digits for the ten thousand digit. This leaves us with 4 digits for the thousands digit, 3 for the hundreds digit

Of the 4 combinations with a 0, similarly we have 5 X 4 X 3 possibilities for the rest of the digits.

8 * 4 * 4* 3 + 4 * 5 * 4 * 3

= 32 * 12 + 20 * 12

= 52 * 12

= 624

There are 624 possible numbers.