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?

Swimminga.

SOLUTION

Because the swimmers can finish first, second, or third, order is important. So the possibilities can be counted by evaluating 8P3.

a.

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?

Trackb.

Order is not important in choosing the team members, so the possibilities can be counted by evaluating 6C4

b.

SOLUTION

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 Toppings7.

Order is not important in choosing the team members, so the combination possibilities can be counted by evaluating 12C3.

SOLUTION

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.

SOLUTION

Because they elect a president and a vice president order is important. So the permutation possibilities can be counted by evaluating 15P2.