In a certain warehouse, each product is given a code consisting of two letters followed by two digits. If the two letters must be identical and the product of the two digits must be even, how many possible codes exist?

Answer Choices

Correct answer marked below

250

650

1950

Correct

2600

67700

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Explanation

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Official Explanation

Official

The 2 letters are identical so basically we can choose 1 (of 26 letters), which shows 26 ways.

Let's see how many digit pairs could be chosen so that their product is even.

Solution 1:

- There are 10 ways to choose each digit (0-9), so the ways to choose 2 digits is

10 \times 10 = 100

ways.

- There are 5 ways to choose an odd digit (1,3,5,7,9), so the ways to choose 2 odd digits (odd product) is

5 \times 5 = 25

ways.

- Therefore there are

100 - 25 = 75

ways to choose 2 digits with an even product.…

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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.