How many subsets of five elements can be formed from a set of 80 elements?

1 Answer
Feb 25, 2017

Answer:

#""^80 C_5 = 24040016#

Explanation:

If we were to pick the #5# elements one at a time, then there would be #80# ways to pick the first, #79# to pick the second, #78# to pick the third, #77# to pick the fourth and #76# to pick the fifth.

That is: #""^80 P_5 = (80!)/((80-5)!) = (80!)/(75!)= 80*79*78*77*76#

But the order in which we pick a particular subset does not matter, so we can divide this value by the number of ways of ordering #5# items, that is #5!#, to get:

#""^80C_5 = (80!)/(75!5!) = (80*79*78*77*76)/(5*4*3*2*1) = 24040016#