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!

THANKS