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?

Explanation

To solve the problem of finding the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, and 5 without repetition, and to determine how many of these numbers will be even, we can follow these steps:

### Step 1: Calculate Total 4-Digit Numbers
We need to choose 4 digits from the 5 available digits (1, 2, 3, 4, 5) and arrange them. The number of ways to arrange \( r \) items from \( n \) items is given by the permutation formula \( P(n, r) = \frac{n!}{(n - r)!} \).

Here, \( n = 5 \) (the digits 1, 2, 3, 4, 5) and \( r = 4 \) (since we want to form 4-digit numbers).

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