EXAMPLE 3

1. Swimming a. There are 8swimmers in the 400 meter freestyle race. In how many ways can the swimmers finish first, second, and third? SOLUTION a. Because the swimmers can finish first, second, or third, order is important. So the possibilities can be counted by evaluating 8P3. EXAMPLE3 Permutations and Combinations Tell whether the possibilities can be counted using a permutation or combination. Then write an expression for the number of possibilities.

2. Track Order is not important in choosing the team members, so the possibilities can be counted by evaluating 6C4 b. b. Your track team has 6 runners available for the 4 person relay event. How many different 4 person teams can be chosen? SOLUTION EXAMPLE 3 Permutations and Combinations

3. Pizza Toppings 7. A pizza shop offers 12 different pizza toppings. How many different 3-topping pizzas are possible? SOLUTION Order is not important in choosing the team members, so the combination possibilities can be counted by evaluating 12C3. for Example 3 GUIDED PRACTICE Tell whether the possibilities can be counted using a permutation or combination. Then write an expression for the number of possibilities.

4. Student Council 8. There are 15 members on the student council. In how many ways can they elect a president and a vice president for the council? SOLUTION Because they elect a president and a vice president order is important. So the permutation possibilities can be counted by evaluating 15P2. for Example 3 GUIDED PRACTICE