If 12 people are playing in a tournament and each person plays every other person, how many games will be played?
The first person plays 11, the second plays 10, the thrid plays 9
number games=11+10+9+...+1
the sum of numbers from n-1 to 1, or
number= N*(n-1)/2=12*11/2= 66
number of subsets of 2 elements from a sample space of 12
= C(12,2) = 66
66 people. Just do 132 / 2.
n*(n-1)/2
To find out how many games will be played in the tournament, we need to determine the total number of unique pairs of players.
In this scenario, we have 12 players. If each player has to play against every other player, we can visualize this as a complete graph, where each player is connected to every other player.
To find the number of pairs, we use the formula for combinations, denoted as "nC2" or "n choose 2." It represents the number of ways to choose 2 items from a group of "n" items without repetition. In our case, "n" is the number of players.
So, for 12 players, we can calculate it as:
12C2 = (12!)/(2!(12-2)!) = (12 * 11)/(2 * 1) = 66
Therefore, there will be 66 games played in the tournament.