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.

1 Answer
Dec 19, 2017

#28#

Explanation:

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.