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What this combinatorics interview question tests

This is a straightforward combinatorics problem that appears in quant interviews to check whether you can quickly count permutations with repeated elements. It rewards accuracy and clear reasoning over complex insight.

To solve problems of this type, you identify the total number of positions available, count how many times each distinct letter appears, and apply the multinomial coefficient formula. The key is careful bookkeeping: missing or miscounting a repeated letter is a common mistake that leads to a wrong answer. Interviewers expect you to show your work and verify your letter inventory before you calculate.

• Permutations with repetition and the multinomial coefficient
• Factorials and simplification
• Systematic enumeration of distinct elements