gen-explain-permutations-and-combinations-as-you-would-to-a-capa-2890

Explain permutations and combinations as you would to a capable student, in 3-4 sentences.

# Permutations and Combinations **Permutations** count the number of ways to arrange items where **order matters** — like assigning gold, silver, and bronze medals to 3 people out of 10 competitors (10 × 9 × 8 = 720 ways). **Combinations** count the number of ways to select items where **order doesn't matter** — like choosing 3 people out of 10 for a committee, where {Alice, Bob, Carol} is the same group as {Carol, Alice, Bob}. The key difference: permutations divide into fewer groups because ABC and BAC are considered different, while combinations treat them as identical selections. Use permutations for arrangements and rankings; use combinations for selections and groups.