Question

Mike is picking out 4 books to read out of collection of 12. How many ways can the books be picked?

Answer 1

3 sets or it you could divide which would still give you 3

Answer 2

You have to choose 4 books out of 12 books. You can choose any 4 books.

You can do that in 12C4 ways.

${}^{12} C_4 = \frac{12!}{4! \times (12 - 4)!} \\ \\ = \frac{12!}{4! \times 8!} \\ \\ = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} \\ \\ = 495$

You can choose 4 books in 495 ways.