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Warm Up Solutions

Solve without a calculator. Show your work.

$\frac{12!}{2! (12 - 2)!} = \frac{\overset{6}{12} \cdot 11 \cdot 10!}{(2 \cdot 1) (10!)} = 66$

$\frac{12!}{3! (12 - 3)!} = \frac{\overset{2}{12} \cdot 11 \cdot 10 \cdot 9!}{(3 \cdot 2 \cdot 1) (9!)} = 220$

Note

Q: What is the difference between a permutation and a combination?

A: The order matters in a permutation, and order does not matter in a combination.