If a code can be either 3 letters followed by 3 digits or 3 digits followed by 3 letters, with no repetition of characters, how many unique codes are possible?

Instruction: Use 26 uppercase letters A–Z and ten digits 0–9. A code is either LLLDDD or DDDLLL. Letters and digits cannot repeat within a code, but a digit block may start with zero. Calculate the total count.

Context: This question assesses the candidate's understanding of permutations and their ability to calculate the total number of unique arrangements under specified conditions.

Updated

Official answer

Assume 26 uppercase letters A–Z and digits 0–9, with no repeated letters or digits; a digit block may start with zero. For the letters-first format, the count is 26×25×24×10×9×8 = 11232000.

The digits-first format has the same count. The formats are disjoint because the first character is a letter in one and a digit in the other. Therefore the total is 2×11232000 = 22464000 codes.

The original single-format count must not be reported as the two-format total. If leading zeroes or letter case have different rules, adjust the relevant factors. This is a count of strings, not a security-strength guarantee.

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