# How many ways can you choose four numbers for a lottery if there are 50 numbers to choose from?

230, 300

#### Explanation:

This is a combinations question - we don't care what order we pick the lottery numbers - just that we have a set of numbers that (we hope) will win the lottery.

The general formula for doing combinations is:

C_(n,k)=(n!)/((k)!(n-k)!) with $n = \text{population", k="picks}$

Substituting in:

C_(50,4)=(50!)/((4)!(50-4)!)=(50!)/((4!)(46!))=>

(50xx49xxcancelcolor(red)48^2xx47xxcancelcolor(blue)(46!))/(cancelcolor(red)(4xx3xx2)xxcancelcolor(blue)(46!))=>

$50 \times 49 \times 2 \times 47 = 230 , 300$