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

Feb 25, 2017

""^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