Permutation & combination

We can select only the first and last digit and permute the remaining three numbers,

1/ First digit 1 and the last digit can be 0, 2 or 4. For each last digit we have to permute 3 remaining digits. This gives a total of 3!x3 = 18 numbers. For example, 10324.

2/With first digit as 2, the last digit can be 0 and 4 only. This gives 3!x2 = 12 numbers.

3/With first digit as 3, the last digit can be 0, 2 and 4. This gives 3!x3 = 18 numbers.

4/With first digit as 4, the last digit can be 0 and 2. This gives 3!x2 = 12 numbers.

Hence the total even numbers are 18+12+18+12 = 60

Regards,

Team,

TopperLearning.