Question

There are 40 numbers in the Louisiana Lotto game. In how many ways can a player select six of the numbers?

Answer 1

`3,838,380`

Explanation:

This is a combinations question - we don't care in what order the numbers are selected. The general formula for a combination is:

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

`C_(40,k)=(40!)/((6)!(40-6)!)=(40!)/((6!)(34!))=>`

`(cancelcolor(blue)40^2xx39xx38xx37xxcancelcolor(brown)36xx35xxcancelcolor(red)(34!))/(cancelcolor(brown)6xxcancelcolor(blue)(5xx4)xxcancelcolor(brown)(3xx2)xxcancelcolor(red)(34!))=>`

`2xx39xx38xx37xx35=3,838,380`