1. WUE
Seventeen applicants want to interview with SAS. In how many ways can the 8 time slots be assigned?
How many different ways can the letters of the word BOOKKEEPER be arranged?
There are 12 finalists in an archery competition. How many ways can the gold, silver & bronze medals be awarded?

2. Today, we are going to talk about COMBINATIONS!!

3. Combinations Order does not matter
The number of combinations of n items of a set chosen r items at a time is
C =

4. Wait… isn’t there a way to do this on the calculator?!

5. Example
There are seven books on your summer reading list. How many ways can you choose five books to read?

6. Example
A reading list has 20 books on it. In how many ways can you choose four books to read?

7. Your Turn…
Of the 20 books on the reading list, in how many ways can you choose seven books?
In how many ways can three pizza toppings be chosen from 12 available toppings?
In how many ways can seven students from a class of 30 be chosen for a field trip?

8. Permutation vs. Combination
Permutations
Combinations
Order matters
Key Words
Arrange
Line up
Order
Use factorials, P(n, r), or multiplication counting principle
without repeats with repeats
Order doesn’t matter
Key Words
Choose
Select
Pick
Use C(n, r)
Permutation vs. Combination

9. Permutation or Combination?
4 books pulled at random from a shelf
12 books arranged on a shelf
3 flavors of juice selected from a variety pack
Remember, a permutation is an ice cream cone….
but a combination is an ice cream bowl!

10. Permutation or Combination? Then answer the question.
It’s election time at a high school that has a total of 50 students in the junior class. How many ways can a class president, class vice president, class treasurer, and class secretary be chosen if each student may only hold one office?
The same class of 50 students wants to form a prom committee. How many ways can a four person prom committee be selected from the junior class?
If we want to form a group of five students and we have 20 to choose from, how many ways is this possible?