Q1:

We've got

8! / (3! * 3! * 2!) total arrangements

To find the ones in which the yellow cars are together, treat them as one car, so we have 7 total, with 3 red and 3 blue.

7! / (3! * 3!) invalid arrangements

So our total is 8!/(3!*3!*2!) - 7!/(3!*3!), or 420.

Q2:

This is a tough one, partly because it's ambiguous: does it mean that all three can't be together in a row, or that any two can't be together? I'm going to assume it means that no two can be adjacent.

We've got 8! arrangements with no restrictions, so we'll start there.

If the bio and history books are together, we'll treat them as one item. Then we have 7! * 2 ways of arranging our 7 books: 7 because we've counting bio+history as one book, and *2 because even though the bio and history count as one book, they can be arranged in two ways next to each other in their space (bio on the left or history on the left).

Bio+programming and history+programming would be the same: 7! * 2 arrangements each.

Now we have to add back bio+history+programming all together, since we've subtracted these arrangements from each of our three pairs above. Here we have six books (since we're treating these three books as one), and we can arrange them in their space in six ways. That gives us 6! * 6.

In all, then, we have

8! - 7!*2 - 7!*2 - 7!*2 + 6!*6, or 14,400.