How many 5-digit numbers divisible by 25 can be created using the digits 0, 1, 2, 3, 4, and 5, when all five digits are used?

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Official Explanation

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To determine how many 5-digit numbers can be formed that are divisible by 25, we need to consider the last two digits, which must be either 25 or 50. For Case 1, where the last two digits are 25, we have 3 choices for the ten-thousands place (1, 3, or 4), 3 choices for the thousands place (any of the remaining digits), and 2 choices for the hundreds place (from the remaining digits). Thus, the total for this case is…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.