OpenStudy (anonymous):

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

5 years ago
Directrix (directrix):

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

5 years ago
OpenStudy (anonymous):

no

5 years ago
Directrix (directrix):

Have you heard of them?

5 years ago
OpenStudy (anonymous):

very vaguely

5 years ago
Directrix (directrix):

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.

5 years ago
Directrix (directrix):

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.

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (anonymous):

wait, nvrm, they're the same

5 years ago
OpenStudy (anonymous):

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

5 years ago