1. EXAMPLE 3 Permutations and Combinations Tell whether the possibilities can be counted using a permutation or combination. Then write an expression for the number of possibilities. There are 8 swimmers in the 400 meter freestyle race. In how many ways can the swimmers finish first, second, and third? Swimming a. SOLUTION Because the swimmers can finish first, second, or third, order is important. So the possibilities can be counted by evaluating 8 P 3. a.

2. EXAMPLE 3 Permutations and Combinations Your track team has 6 runners available for the 4 person relay event. How many different 4 person teams can be chosen? Track b. Order is not important in choosing the team members, so the possibilities can be counted by evaluating 6 C 4 b. SOLUTION

3. GUIDED PRACTICE for Example 3 Tell whether the possibilities can be counted using a permutation or combination. Then write an expression for the number of possibilities. A pizza shop offers 12 different pizza toppings. How many different 3- topping pizzas are possible? Pizza Toppings 7.7. Order is not important in choosing the team members, so the combination possibilities can be counted by evaluating 12 C 3. SOLUTION

4. GUIDED PRACTICE for Example 3 Student Council There are 15 members on the student council. In how many ways can they elect a president and a vice president for the council? 8.8. SOLUTION Because they elect a president and a vice president order is important. So the permutation possibilities can be counted by evaluating 15 P 2.