A small acting club has 8 members. Two of the members are to be chosen for a trip to see a Broadway play. How many different 2 -member groups are possible?

Question

A small acting club has 8 members. Two of the members are to be chosen for a trip to see a Broadway play. How many different 2-member groups are possible?

Answer 1

If there are 8 members, assign each person a letter, such as A-H. Then align them up as follows:

 

A. B  C D E F G H

 

Start with A and move down the line:

 

AB, AC, AD, AE, AF, AG, AH.

 

you can see the pattern here. Now you start with B and move DOWN the line because if you pair A with  B you get a duplicate which you don't need.  Follow suit for the rest of the letters.  Your total is:

7 + 6 + 5 + 4 + 3 + 2 + 1 = 30 possible 2- member teams.

Answer 2

Johnny/Tammy,

 

It is 28 2 member teams..while adding you added 2 extra.

 

Another way is P(8,2) = 8!/((8-2)!*2!) = 8*7/2 = 28