Algebra 2 / Unit 9: Probability
9.2 Permutations
Notes
A permutation is an arrangement where order matters.
- $n! = n(n - 1)(n - 2)\cdots 1$, and $0! = 1$.
- Arrange $r$ of $n$ items: $\displaystyle _nP_r = \frac{n!}{(n - r)!}$.
- With repeated items, divide by the factorial of each repeat count: "LEVEL" has $\displaystyle \frac{5!}{2!\,2!} = 30$ arrangements.
- Example: choosing a president, vice president and secretary from 6 people: $_6P_3 = 6 \cdot 5 \cdot 4 = 120$.
Practice
Evaluate $_8P_3$.
$8 \cdot 7 \cdot 6 = 336$.
How many different arrangements of the letters in "BOOK" are there?
$\displaystyle \frac{4!}{2!} = 12$ because the two O's are identical.
In a race of 10 runners, how many ways can gold, silver and bronze be awarded?
Order matters: $10 \cdot 9 \cdot 8 = 720$.
Ready for more? Take the Unit 9 test.