The coach of a soccer team is holding tryouts and can take only 3 more players for the team. There are 6 players trying out. How many different groups of 3 players could possibly be chosen?
To find the number of different groups of 3 players that could be chosen, we need to use the concept 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 players and r is the number of players to be chosen.
In this case, there are 6 players trying out and the coach can take only 3 more players for the team. So we need to find the number of combinations of 6 players taken 3 at a time, which is denoted as C(6, 3).
Now, let's calculate the answer step by step:
Step 1: Calculate the factorial of 6.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Step 2: Calculate the factorial of 3.
3! = 3 x 2 x 1 = 6
Step 3: Calculate the factorial of (6-3), which is 3.
(6-3)! = 3! = 3 x 2 x 1 = 6
Step 4: Substitute the values into the formula for combinations:
C(6, 3) = 6! / (3! * (6-3)!)
= 720 / (6 * 6)
= 720 / 36
= 20
Therefore, there are 20 different groups of 3 players that could possibly be chosen by the coach.