Question

15. A board game has 5 different pieces. Players can choose a boat, a car, a top

hat, a shoe, and a dog. Ayers randomly selects one of the pieces, and then Nolan
randomly selects one of the remaining pieces. State how many combinations are
possible and list each possible combination that Ayers and Nolan could choose.

Answer 1

5P2 = 5! / (5-2)!
= 5! / 3!
= (5 * 4 * 3!) / 3!
= 5 * 4
= 20

Therefore, there are 20 possible combinations that Ayers and Nolan could choose.

The list of possible combinations is as follows:

Boat - Car
Boat - Top Hat
Boat - Shoe
Boat - Dog
Car - Boat
Car - Top Hat
Car - Shoe
Car - Dog
Top Hat - Boat
Top Hat - Car
Top Hat - Shoe
Top Hat - Dog
Shoe - Boat
Shoe - Car
Shoe - Top Hat
Shoe - Dog
Dog - Boat
Dog - Car
Dog - Top Hat
Dog - Shoe
These are the 20 possible combinations that Ayers and Nolan could choose from the set of 5 different pieces.