Question

Troy is hosting a game night. There are 6 card games and 7 board games to choose from. For the role-playing game, Troy has 2 options. If Troy and his friends want to play one of each type of game, in how many different ways can they choose the games?

a) 72 ways
b) 84 ways
c) 90 ways
d) 96 ways

Answer 1

To determine the number of ways in which Troy and his friends can choose one card game, one board game, and one role-playing game, you multiply the number of options for each category together. The result is 84 different ways to pick the games for the game night.

Step-by-step explanation:

The question revolves around the concept of counting the number of ways different games can be chosen given specific constraints. Troy has 6 card games, 7 board games, and 2 options for the role-playing game. To find the total number of different ways one of each type of game can be selected, we multiply the number of choices for each category:

Number of ways to pick a card game: 6
Number of ways to pick a board game: 7
Number of ways to pick a role-playing game: 2

To get the total number of combinations we use the fundamental counting principle, multiplying these numbers:

6 (card games) × 7 (board games) × 2 (role-playing games) = 84 total ways

So, Troy and his friends can choose the games in 84 different ways.