Question

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

Answer 1

`""^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`