Question

The coach of a softball 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?

Answer 1

20 different groups of 3 players could possibly be chosen .

Step-by-step explanation:

Here we have , The coach of a softball team is holding tryouts and can take only 3 more players for the team. There are 6 players trying out. We need to find  How many different groups of 3 players could possibly be chosen .Let's find out:

Given scenario in question is as coach needs to select 3 players out of 6 players left , and we will use combination concept to find the number of possible combinations he could have to choose players .

We know that formula for combination is :

⇒ $nC_r=\frac{n!}{r!(n-r)!}$

Here n=6 , r=3

⇒ $6C_3=\frac{6!}{3!(6-3)!}$

⇒ $6C_3=\frac{6(5)(4)3!}{3!(3)(2)}$

⇒ $6C_3=\frac{6(5)(4)}{(3)(2)}$

⇒ $6C_3=5(4)$

⇒ $6C_3=20$

Therefore , 20 different groups of 3 players could possibly be chosen .