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

1 Answer

Answer:

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="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!))=>#

#50xx49xx2xx47=230,300#