How many 4-digit even numbers are there with distinct digits?

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Correct answer marked below

2250

2296

Correct

2520

4499

4500

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Explanation

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Official Explanation

Official

We need to count 4-digit even numbers with distinct digits.

Case 1: The last digit is 0.

The number is of the form _ _ _ 0.

First digit (thousands place) cannot be 0, so choices = 9 digits (1-9).

Second digit: any of the remaining 8 digits (excluding the first digit and 0).

Third digit: any of the remaining 7 digits.

Last digit is fixed as 0.

Count =

9 \times 8 \times 7 \times 1 = 504

.

Case 2: The last digit is 2, 4, 6, or 8 (4 possibilities).

The number is of the form _ _ _ (even digit).…

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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.