Question

How many different selections of 4 books can be made from a bookcase displaying 12 books?

Answer 1

`495`

Explanation:

`color(white)("X")_(12)C_4 = (12!)/((12-4)!*4!) = (cancel(12)xx11xxcancel(10)^5xx9)/(cancel(4)xxcancel(3)xxcancel(2)xx1) = 495`

For each of the `12` choices that could be made for the first book
there would be `11` choices that could be made for the second book
then `10` choices for the third
and `9` choices for the fourth.

So there would be `12xx11xx10xx9` ways of selecting the books
but the same 4 books could have been selected in `4xx3xx2xx1` different ways (using the same logic as above).

So the actual number of different selections would be:
`color(white)("XXX") (12xx11xx10xx9)/(4xx3xx2xx1)`