How many even 3-digit positive integers can be written using the digits 1,2,4,7, and 8?

Looking at the question, we can see we have 5 different numbers that can go in any order.

5 * 4 * 3

The above is basically saying there are 5 different numbers that can be multiplied by 4 other numbers. Those 2 can be multiplied by 3 different ones, leaving us with a 3 digit positive integer.

5 * 4 * 3 = 60