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Permutations and combinations – Problem solving with permutations and combinations

📘 Notes

Problem Solving with Permutations and Combinations

The key to solving problems is deciding whether order matters.

1. Identifying the Method

Situation Method
Objects arranged Permutation
Objects selected Combination

2. Example (Permutation)

How many ways can gold, silver and bronze medals be awarded among 6 athletes?

\[ ^6P_3=\frac{6!}{3!}=120 \]

3. Example (Combination)

How many committees of 3 students can be formed from 6 students?

\[ ^6C_3=\frac{6!}{3!3!} \] \[ =20 \]

4. Permutations with Repeated Objects

If there are repeated objects:

\[ \frac{n!}{p!q!r!\dots} \]

Example: arrangements of the word LEVEL

\[ \frac{5!}{2!2!}=30 \]