five friends plan a chess tournament. how many possible games can be played if each person plays with each other person exactly once.
each of 5 people plays 4 others.
That's 5*4
But, that counts each person twice, so you really have
5*4/2 = 10 games
10
To find the total number of possible games that can be played, we can use a combination formula. In this case, since each person plays with each other person exactly once, we need to find the number of combinations of 2 people from a group of 5. Here's how you can calculate it:
Step 1: Determine the number of combinations
The formula for finding the number of combinations is given by:
C(n, r) = n! / (r! * (n-r)!)
Where:
n is the total number of elements (in this case, 5 friends)
r is the number of elements taken at a time (in this case, 2 people needed for a game)
! represents the factorial of a number which means multiplying that number with all the positive integers less than it down to 1.
Step 2: Plug in the values
Substitute the values into the formula:
C(5, 2) = 5! / (2! * (5-2)!)
Step 3: Simplify
Simplify the factorial expressions:
C(5, 2) = (5 * 4 * 3 * 2 * 1) / ((2 * 1) * (3 * 2 * 1))
C(5, 2) = (5 * 4) / (2 * 1)
C(5, 2) = 10
Therefore, there are a total of 10 possible games that can be played in the chess tournament.