How many different three-member teams can be formed from six students?

1 Answer
Dec 13, 2015

There are #20# ways to choose 3 students from a group of 6 students.

Explanation:

For this question, you need to choose #3# students from a group of #6# students. Since no two students are the same, you will need to determine the number of combinations.

To do so, simply do #(n!)/(r!(n-r)!)# where #n# is the number of students total and #r# is the number of students that need to be chosen.

Plugging in, we get:

#(6!)/(3!(6-3)!)#
#=(6*5*4*3*2*1)/((3*2*1)(3!))#
#=(6*5*4*cancel(3*2*1))/(cancel((3*2*1))(3*2*1))#
#=5*4#
#=20#

So, there are #20# ways to choose 3 students from a group of 6 students.