Solve the following problems using the strategies you have learned in this section.
You have a team of 5 people and 3 tasks to assign. Task A needs two people, Task B needs two people, and Task C needs one person. You are only going to assign one task to each person. In how many different ways can you assign the tasks?
Alina and Adam are making boxes of truffles to give out as wedding favors. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types, how many different boxes can they make?
A men’s basketball league assigns every player a two-digit number for the back of his jersey. If the league uses only the digits 1–5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit (e.g., 22), and no two players have the same number?
A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?
A delegation from Gotham City goes to Metropolis to discuss a limited Batman–Superman partnership. If the mayor of Metropolis chooses 3 members of the 7-person delegation to meet with Superman, how many different 3-person combinations can he choose?
Mario’s Pizza has 2 choices of crust: deep dish crust or thin crust. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions, and pepperoni. The order of the toppings on top of the pizza doesn't matter. Finally, Mario’s offers every pizza in extra cheese as well as regular. If Linda’s volleyball team decides to order a pizza with 4 unique toppings, how many different choices do the teammates have at Mario’s Pizza?
Country X has a four-digit postal code assigned to each town, such that the first digit is non-zero, and none of the digits is repeated.
| Quantity A | Quantity B |
| The number of possible postal codes in Country X |
4,500 |
Eight athletes compete in a race in which a gold, a silver and a bronze medal will be awarded to the top three finishers, in that order.
| Quantity A | Quantity B |
| The number of ways in which the medals can be awarded |
8 × 3! |
Lothar has 6 stamps from Utopia and 4 stamps from Cornucopia in his collection. He will give two stamps of each type to his friend Peggy Sue.
| Quantity A | Quantity B |
| The number of ways Lothar can give 4 stamps (two of each type) to Peggy Sue |
100 |