Question

A small acting club have 7 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

So let's name the 7 members by letters A,B,C,D,E,F,G so the combinations could be
AB,AC,AD,AE etc. so there r 36 options but if don't count the ones like AB and BA that include the same people u have 19 answers

Answer 2

Using the combination formula, it is found that 21 groups are possible.

The order in which the members are selected is not important, for example, Elisa and Chanel is the same group as Chanel and Elisa, hence the combination formula is used.

Combination formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, 2 members are chosen from a set of 7, hence:

$C_{7,2} = \frac{7!}{2!5!} = 21$

21 groups are possible.

For more on the combination formula, you can check https://brainly.com/question/25821700