The key to solving problems is deciding whether order matters.
| Situation | Method |
|---|---|
| Objects arranged | Permutation |
| Objects selected | Combination |
How many ways can gold, silver and bronze medals be awarded among 6 athletes?
\[ ^6P_3=\frac{6!}{3!}=120 \]How many committees of 3 students can be formed from 6 students?
\[ ^6C_3=\frac{6!}{3!3!} \] \[ =20 \]If there are repeated objects:
\[ \frac{n!}{p!q!r!\dots} \]Example: arrangements of the word LEVEL
\[ \frac{5!}{2!2!}=30 \]