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

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Answer 1 · 2017-12-19T20:17:29

#28#

The number must end with #2# or #4#, yielding two choices. Then the remaining digits are #1#, #3#, #5# and an even digit less than #5#.

Three digit numbers: Having chosen #2# or #4# for the last digit, there are #3# admissible possibilities for the first digit, namely #1#, #3# or whichever of #2# or #4# is left. Finally, any of the #3# remaining digits can be used for the middle digit. So there are #2xx3xx3 = 18# possible #3# digit numbers.
Two digit numbers: Having chosen #2# or #4# for the last digit, there are #4# possibilities for the first digit, so a total of #2xx4 = 8# possibly #2# digit numbers.
One digit numbers: #2# or #4#, which makes #2# possibilities.

So there are a total of #18+8+2 = 28# possible numbers satisfying the criteria.