How many ways can you get a bunch of 4 books to give a friend if you have 30 books (15 novels, 10 history book and 5 math books)?

Answer 1

Without any constraints, you have 30 to choose from for the first, 29 for the second, 28 for the third, and 27 for the fourth.
But there are 4! ways to choose the same 4 books, so using the multiplication principle, the number of ways to find 4 books is
30*29*28*27/4!
=30!/(4!(30-4)!)
=C(30,4)
The last line is a "function" called combination, or n choose r, where we choose r objects from n, and order of choice is not important.