How many even 4-digit numbers can be formed using the digits 1, 2, 3, 4 and 5 if no digit is repeated within a number?

The units digit must be even, so it is 2 or 4 — 2 choices. The remaining three places are filled from the other 4 digits in $4\times 3\times$ 2 = 24 ways. Total = $2\times 24=48$. (The value $120=P(5,4)$ counts all 4-digit numbers, odd ones included.)