A password is made by arranging 2 distinct letters followed by 2 distinct digits (0-9). How many such passwords can be created?

Instruction: Use only the 26 lowercase English letters and digits 0 through 9. Form two different letters followed by two different digits; 0 is allowed in either digit position. Count the strings, keeping character order significant.

Context: This question tests the candidate's understanding of permutations involving both letters and numbers.

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Official answer

There are 26 × 25 × 10 × 9 = 58,500 passwords.

The first two positions use two different letters from the 26-letter alphabet; the final two use different digits from 0 through 9. The digit 0 is allowed in either digit position, so the first digit has 10 choices. Multiply choices across positions because every allowed partial string has the stated number of extensions.

This is ordered counting: ab12 and ba12 are different strings. A combination count would discard that order. If letter repetition were permitted, the count would be 26 × 26 × 10 × 9 = 60,840.

Assessment: A correct answer states the character set, preserves order and verifies the arithmetic. Counting a search space does not establish that this short format is a secure password policy.

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