Combinations problem

Here is the problem:

"Winston must choose 4 classes for his final semester of school. He must take at least 1 science class and at least 1 arts class. If his school offers 4 (distinct) science classes, 3 (distinct) arts classes and 3 other (distinct) classes, how many different choices for classes does he have?"

I'm wondering what's wrong with the following method:

(4x3) choices of first (compulsory) art class and science classes

x

8c2 choices of remaining courses

total 336 (correct answer is 160)?

Thanks

Thanks

A reasonably efficient method would be to use inclusion/exclusion.

How many possible choices with no restrictions?

Subtract the number of choices with "no science".

Subtract the number of choices with "no art".

Then add the number of choices with "no art and no science". (There are actually none in this latter category.)

Thanks for that I've just about got to grips with the PIE now.