Find the number of 4-digit numbers that can be formed using the digits 1,2,3,4,5 if no digit is repeated. How many of these will be even?

Unit place can be filled using any one of the digits 1,2,3,4 and 5 in 5 ways.
Tenth place can be filled in 4 ways
Hundredth place can be filled in 3 ways
Thousandth place can be filled in 2 ways
Therefore total number of ways = 5 x 4 x 3 x 2 = 120 numbers.
Number of even numbers = Unit digit can be filled in only 2 ways.
And the other, place can be filled in the way as specified above.
Therefore total number of even numbers will be = 2 x 4 x 3 x 2 = 48 numbers.