The number of five-digit numbers divisible by 5 that can be formed using the numbers 0, 1, 2, 3, 4, 5 without repetition is:

• A) 240
• B) 216
• C) 120
• D) 96

To find the number of five-digit numbers divisible by 5 that can be formed using the digits 0, 1, 2, 3, 4, and 5 without repetition, we need to consider the rules for divisibility by 5. A number is divisible by 5 if it ends in either 0 or 5.

Case 1: Last Digit is 0

If the last digit is 0, the first digit can be any of the remaining digits (1, 2, 3, 4, 5). This gives us 5 options for the first digit. After selecting the first digit, we have 4 digits left to choose from for the second, third, and fourth positions.

• Choices for the first digit: 5 options
• Choices for the second digit: 4 options
• Choices for the third digit: 3 options
• Choices for the fourth digit: 2 options

The total combinations for this case are:

5 × 4 × 3 × 2 = 120

Case 2: Last Digit is 5

If the last digit is 5, the first digit can be any of the remaining digits (1, 2, 3, 4, 0). Here, we have 4 options for the first digit (it cannot be 0). After selecting the first digit, we have 4 digits left to choose from for the second, third, and fourth positions.

• Choices for the first digit: 4 options
• Choices for the second digit: 4 options
• Choices for the third digit: 3 options
• Choices for the fourth digit: 2 options

The total combinations for this case are:

4 × 4 × 3 × 2 = 96

Final Calculation

Now, we add the totals from both cases:

120 (last digit 0) + 96 (last digit 5) = 216

Thus, the total number of five-digit numbers divisible by 5 that can be formed is 216. The correct answer is B) 216.