One way to look at it is to account for that pesky person who is in both clubs.
Draw a Venn and it will be easier to see.
Hi, I can't seem to answer this question. The answer I get differs from the back of the book and I don't understand why.
Q: The camera club has 5 members, and the math club has 8. There is only 1 member common to both clubs. In how many ways could a committee of 4 people be formed with a least one member from each club?
I think the part where I'm going wrong is where the 1 member overlaps. I'm not sure how I'm suppose to deal with it. The answer I get is 470 while the answer at the back is 459...
If someone could please show me how I'm suppose to go about solving this problem, it would be great!
But what if I decided to include the pesky person on the other side first then the first side. As in:
The answer then becomes 456
Here's how I solved it directly. There are 4 people in club 1 and 7 in club 2 and the one guy on the side who can count for both. Now, we either choose to include the one guy in the committee or not. If we don't choose him, then there are
ways to pick the committee. That is, we would like to pick out k from one group and the rest from the other, and note that k is from 1 to 3, so one person has to be chosen from each group.
Now we concern ourselves with the person who's in both camps. We've picked him, so we need to pick 3 other people. They can belong to any club since the one person counts from both camps. Thus we add
to the above. Evaluating that will give you 459 as the book says.