4-digit numbers are to be formed using the digits, 1, 2, 3, 4, and 5.
There will be as many 4-digit numbers as there are permutations of 5 different digits taken 4 at a time.
Therefore, required number of 4 digit numbers
Among the 4-digit numbers formed by using the digits, 1, 2, 3, 4, 5, even numbers end with either 2 or 4.
The number of ways in which units place is filled with digits is 2.
Since the digits are not repeated and the units place is already occupied with a digit (which is even), the remaining places are to be filled by the remaining 4 digits. Therefore, the number of ways in which the remaining places can be filled is the permutation of 4 different digits taken 3 at a time.
Number of ways of filling the remaining places
= 4 × 3 × 2 × 1 = 24
Thus, by multiplication principle, the required number of even numbers is 24 × 2 = 48
