Question

The students in Mr. Trumbull's English class need to read 2 books from a list of 7 books. How many different combinations of books are possible?

Answer 1

For problems like this, we need to first decide whether to use the combination formula `color(white)(2)_nC_r` or the permutation formula `color(white)(2)_nP_r`.

Here is the difference:

We use the permutation formula when order matters, but when order doesn't matter we use the combination formula.

Thinking about our problem, we come to the conclusion that order does not matter, therefore we use the combination formula.

`color(white)(2)_nC_r` means to evaluate using the formula `(n!)/((n - r)!(r)!)`, where n is the total number of elements and r is the number of elements from that set picked at one time. So, in your problem, `n = 7` and `r = 2`

Substituting:

`(7!)/(( 7 - 2)!(2)!)`

`=5040/(240)`

`= 21`

Therefore, there are 21 different combinations of choices of books that are possible.

Hopefully this helps!