Question

How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?

• A. 24
• B. 48
• C. 60
• D. 120

Hint:

For divisibility by 5, the last digit must be 0 or 5. When digits don't include 0, last digit must be 5. Arrange remaining digits without repetition.

Answer 1

The Correct Option is A

The available digits are \(\{1, 2, 3, 4, 5\}\). The 4-digit number must be divisible by 5. Divisibility by 5 requires the last digit to be 0 or 5. As 0 is not available, the last digit must be 5. Step 1: Set the last digit to 5. Step 2: Select and arrange the first three digits from the remaining set \(\{1, 2, 3, 4\}\) without repetition. Step 3: The number of permutations for the first three digits is \( P(4,3) = 4 \times 3 \times 2 = 24 \). Step 4: The total count of such 4-digit numbers is \(24 \times 1 = 24\).