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

$3 , 838 , 380$

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 $n = \text{population", k="picks}$

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!))=>

$2 \times 39 \times 38 \times 37 \times 35 = 3 , 838 , 380$