A summer reading list has 20 books on it. How many ways can you choose 4 books?

Question

directrix · Answer

@SaylorTickels  Do you know combinations and permutations of objects and how to calculate them?

anonymous · Answer

no

directrix · Answer

Have you heard of them?

anonymous · Answer

very vaguely

directrix · Answer

What you want to compute is a combination of 20 books taken 4 at a time. 
That gives you the number of different groups of 4 books from the 20.
C(20,4) --> Think of this as 20 Choose 4.
We'll need the combination formula.

directrix · Answer

If you have not studied combinations, you can think of the problem this way:
There are 20 ways to choose the first book, 19 for the second, 18 for the third, and 17 for the last. That would give 20*19*18*17 ways where order mattered. But, the order of selection is not of importance. So, you would need to divide out the number of ways a given set of four books could be chosen in order. That is 4*3*2*1.

I have said too much but on problems of this type, words are necessary.

Here is your task: Divide (20*19*18*17) by 24 to get the answer you seek.
Note: 24 is the 4*3*2*1 part.

anonymous · Answer

I believe there's more to it than that. A combination such as this one is $$C(20, 4) = \frac{ 20! }{ 4!(20-4)! }$$

anonymous · Answer

wait, nvrm, they're the same

anonymous · Answer

Directrix is using good logic. What I have is the formula definition.