Combinations Worksheet with Answer Key

What's on the worksheet

1. Find each number without working out any large factorial in full.
   \binom{8}{3}{}_{12}C_{4}C(10, 5)\dfrac{\binom{9}{4}}{\binom{9}{5}}\dfrac{\binom{20}{4}}{\binom{20}{3}}
2. Word problem: how many smoothies from 9 fruits, three at a time.
3. Decide in each situation whether order matters for 11 paintings and count.
4. Word problem: how many former teammates took selfies at a robotics reunion.
5. Word problem: committees chosen from 6 juniors and 7 seniors.
6. Word problem: counting hands from a standard 52-card pack.
7. Explain why the numbers in row 14 rise and then repeat in reverse.