Problema Solution
The coach of a soccer team is holding tryouts and can take only 3 more players for the team. There are 4 players trying out. How many different groups of 3 players could possibly be chosen?
Answer provided by our tutors
Since the order of the selected players is not of importance we will use combinations to solve.
The number of p-combinations from a set of n elements is:
In our case p = 3 and n = 7 (7 since 3+4=7)
We need to find the number of 3-combinations from a set of 7 elements:
C(7,3) = 7!/(3!(7-3)!)
C(7, 3) = 7!/(3!4!)
C(7, 3) = (5*6*7)/(2*3)
C(7, 3) = 35
There are 35 different groups of 3 players.