A password has two distinct uppercase letters followed by three distinct digits. If digit (0) cannot be in the first digit-position, how many passwords are possible?

Correct answer: (26 \times 25 \times 9 \times 9 \times 8)

The direct answer is option A, 26 × 25 × 9 × 9 × 8. Apply the multiplication principle: multiply the choices at each successive position. The first uppercase letter has 26 choices. The second must be different, so it has 25 choices. For the first digit position, zero is forbidden, leaving 1 through 9, or 9 choices. The next digit must be distinct from the first, so 9 choices remain, including zero if unused. The last digit then has 8 choices. Thus the total is 26 × 25 × 9 × 9 × 8. Option B allows repeated letters and allows zero first, so it is wrong. Option C wrongly reduces the letter choices and digit choices. Option D incorrectly allows 10 choices for the first digit. Remember: distinct means subtract already used choices; a position-specific restriction must be applied at that position.