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

1 Answer
MathFact-orials.blogspot.com
Feb 27, 2017

#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#

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