MHB Combinations of groups question

[Raerin]

Combinations of groups question [edited question]

The camera club has 5 members and the mathematics club has 8. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club?

I am confused about the "one member common to both clubs" part and that the committee needs to have at least one member from each group. So when calculating do you do it as 5 members in camera club or 4 members since there's one person in both clubs?

 

[Jameson]

"One member common to both clubs" is someone who is in both, so that will affect the question "How many people are there total?". At first glance it might seem like there are 5+8=13 people but how many are there really?

To get a 4 person committee you could do this the by taking people from both groups like so: 1 and 3, 2 and 2 and 3 and 1.

That will get you started. I'll help you address the tricky part if you can do up to here. :)