How many even numbers less than 500 can be formed using the digits 1,2,3,4,5? Each digits may be used only once in any number.

(2, 4, 12, 14, 24, 32, 34, 42, 52, 54, 124, 132, 134, 142, 152, 154, 214, 234, 254, 312, 314, 324, 342, 352, 354, 412, 432, 452) = 28 such numbers

Well we know the digit must end in 2 or 4, because it has to be even. So 1, 3, 5, can't be the ending digit.

We've chosen 2 digits already (2 and 4), so there are 3 possibilities for the first digit. It can't be 5, because then it would exceed the count of 500, so 1, 3, or whatever's left of 2 and 4. And only 3 digits left for the middle digit. So that means 2 * 3 * 3 = 18 cases for 3 digit numbers..

Now what about 2 digit numbers? Having chosen 2 or 4, we have 4 other possibilities left. So 2 * 4 = 8 cases for 2-digit numbers.

We have to remember 1 digit numbers, 2 or 4, so 2 cases.

In the end: 18 + 8 + 2 = 28 numbers.