How many 3 person group can be formed in a club with 8 people?

Hi!

I'm going to make a text diagram.
Each | is a person.

| | | | | | | |

Now seperate into groups of three

| | |

| | |

| |

There are 2 groups of three

The answer is 2.

Hope this helps! :)

The first person in the group can be selected in any one of 8 ways. 
Once selected, the second person can be selected in any one of 7 ways. 
Once the first two are selected, the remaining person can be selected in any one of 6 ways. 

This can be done in a total of 8 x 7 x 6 ways. 

But, since the order in which the people appear in the group is not important, and since 3 people can be arranged in 3 x 2 x 1 = 6 ways, you need to divide the above number by 6 to filter out those groups with the same members (just rearranged). The answer is therefore, 

(8 x 7 x 6) / (3 x 2 x 1) = 56