AS & A Level Maths

Problem Solving with Permutations and Combinations

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

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

Open Full Notes

Open in New Tab

0/0 mastered, 0 attempted

▶ Start Practice 🔁 Review All Questions

0/120 solved, 0 studied

0/120 solved + studied

▶ Start Problems 🔁 Review All Problems