Question

How many different combinations of 5 numbers can be made from 50 (different) numbers?

Answer 1

`2,118,760`

Explanation:

I'm going to answer this assuming that we have 50 different somethings (numbers, symbols, books, whatever) and are choosing combinations of 5 at a time.

The combination general formula is:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

giving

`C_(50,5)=(50!)/((5!)(45!))`

`C_(50,5)=(cancel50^5xx49xxcancel48^4xx47xx46xxcancel(45!))/(cancel((5xx4xx3xx2!))(cancel(45!)))`

`C_(50,5)=5xx49xx4xx47xx46=2,118,760` combinations.