An Amazon merchant is selling baseball hats that come in 4 different colors: black, white, blue, and green. The merchant stocks plenty of each color. You need to buy a total of 14 hats, but at most 5 will be blue. How many different purchases are possible?

Of 12 possible books, you plan to take 6 with you on vacation. How many different collections of 6 books can you take? You can take different collections of 6 books on vacation with you.

You have four pairs of socks, one pair each of red, blue, white, and green. Each morning, you reach into the drawer and pick out two random socks. How many days could go by before you picked exactly the same two colors of socks again?

A university student is selecting courses for his next semester. He can choose from 6 science courses and 10 humanities courses. In how many ways can he choose 9 courses if fewer than 3 must be science courses?