Committee Combinations

What this combinatorics interview question tests

This is a foundational combinatorics problem that appears frequently in quant interview screens. It tests whether you can recognise when to apply combinations rather than permutations, and whether you can compute binomial coefficients accurately under pressure. The simplicity of the setup masks a common source of error: confusing ordered arrangements with unordered selections.

To solve problems in this family, you need to identify whether the order of selection matters. If it doesn't—as with committee membership—you're counting combinations. The key is setting up the correct formula and simplifying without arithmetic mistakes. Interviewers often follow up by varying the constraints: what if certain people must or must not be included, or if roles are distinct?

• Combinations vs. permutations
• Binomial coefficient notation and calculation
• Recognising when order is irrelevant