A computer password consists of 4 characters: 2 letters followed by 2 numbers. If letters can repeat but numbers cannot, how many unique passwords can be created?
Instruction: Use only 26 lowercase English letters and digits 0 through 9. Count strings with two letters followed by two digits: letters may repeat, digits may not, and 0 is allowed in either digit position.
Updated
Official answer
The count is 26 × 26 × 10 × 9 = 60,840.
Each letter position has 26 choices because letters may repeat. The first digit has 10 choices, including 0; the second has 9 because it must differ from the first. The character order is part of the password, so arrangements such as ab12 and ab21 are distinct.
If both digits could also repeat, the count would rise to 26² × 10² = 67,600. If letter repetition were forbidden instead, the original digit restriction would give 26 × 25 × 10 × 9 = 58,500.
Assessment: Identify which positions can repeat and apply the restriction only to the relevant positions. These are counts of permitted strings, not evidence that a four-character password is secure or that users choose uniformly.