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.