posted by Chelsea P on .
the student wants to buy 3 CDs, but assume that there are 3 CDs featuring the piano, 5 CDs featuring the trumpet, and 7 CDs featuring the saxophone. (2) In how many ways can the selection be made if CD's featuring at least 2 different instruments are selected?
There are several ways you can do it, but this way is probably the easiest.
Try selecting 3 CDs from the entire set of CDs, ignoring the other parts of the problem for now. You have 15C3=455 ways.
Then find how many ways they can be chosen so that all three are the same. 3C3+5C3+7C3=46.
Subtract! 455-46 should be your answer, since there's always two different types of instruments!
This is called COMPLEMENTARY COUNTING, and it means that you are counting all possibilities then subtracting the ones you don't want. It's often much easier that way.