How many subsets of four elements can be formed from a set of 100 elements?

1 Answer
Dec 12, 2017

Answer:

#""^100C_4 = 3921225#

Explanation:

If we choose the four elements one at a time, then there are #100# possible choices for the #1#st element, #99# for the #2#nd, #98# for the #3#rd and #97# for the #4#th. Note that it does not matter what order the four items are chosen in, so we then need to divide the total number of choices #100 * 99 * 98 * 97# by the number of ways of arranging #4# items, namely #4! = 4 * 3 * 2 * 1#.

The number of ways of choosing a subset of #4# elements out of #100# is:

#""^100C_4 = (100!)/(96! 4!) = (100 * 99 * 98 * 97) / (4 * 3 * 2 * 1) = 3921225#