The coach of a soccer team is holding tryouts and can take only
3
more players for the team. There are
5
players trying out. How many different groups of
3
players could possibly be chosen?
--See previous post: Sat, 8-5-17, 12:47 PM.
To find the number of different groups of 3 players that can be chosen out of 5 players, we can use the combination formula, which is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of players (5 in this case)
- r is the number of players to be chosen (3 in this case)
- n! represents the factorial of n, which is the product of all positive integers from 1 to n
Now let's calculate the number of combinations:
C(5, 3) = 5! / (3!(5-3)!)
= 5! / (3!2!)
= (5 × 4 × 3!) / (3! × 2 × 1)
= (5 × 4) / (2 × 1)
= 20 / 2
= 10
Therefore, there are 10 different groups of 3 players that could possibly be chosen from the 5 players trying out.