Six people enter a dart throwing tournament in which each person must play each of the others in the tournament exactly once. Determine the total number of games that will be played.

number of games

= C(6,2) = 6(5)/2 = 15

15

To determine the total number of games that will be played in this dart throwing tournament, we need to use the concept of combinations.

In a tournament with 6 people, each person must play against each of the others exactly once. Let's break down the steps to calculate the total number of games:

Step 1: Determine the total number of pairs of players
In a tournament, each game involves two players. To calculate the total number of pairs of players, we can use the combination formula, denoted as C(n, 2), where n represents the number of players.
For this tournament, n = 6.
C(6, 2) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15

Step 2: Determine the number of games per pair
Since each pair of players only plays one game, the number of games per pair is 1.

Step 3: Calculate the total number of games
To calculate the total number of games, we multiply the number of pairs of players by the number of games per pair.
Total number of games = Number of pairs of players * Number of games per pair
Total number of games = 15 * 1 = 15

Therefore, in this dart throwing tournament, a total of 15 games will be played.