How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6 and 7 if no digit is repeated?

Question

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5 and none of the digits is repeated?

Answer 1

60
.
As it is an even number, it must end with 2, 4 or 6.
Taking XX2 there are five combinations for the first digit (1X2, 3X2, 4X2, 6X2, 7X2).
Each digit has 4 combinations (for 1X2, these are 132, 142, 162, 172).
So there are 4 * 5 = 20 combinations for XX2.
XX4 and XX6 have the same amount of combinations, so the total combinations is 3 * 20 = 60.