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

1 Answer
Feb 2, 2016

Answer:

#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)#