Question 1158125
There are 10 ways to pick the first number, 9 ways to pick the second number, and 8 ways to choose the final number, so there are {{{10*9*8=720}}} possible outcomes.
1. There are {{{10^3=1000}}} outcomes.
2. There is a {{{1/720}}} chance of winning. The expected value is {{{(x-5)*(1/720)-5*(719/720)}}}, where x is how much you win if you win the lottery. This simplified to *[invoke solve_equation "(x-5)*(1/720)-5*(719/720)"] <br/> If the expected value is $0, then Illinois will pay you {{{720*5=3600}}} dollars.
3. The expected value is {{{(x-1)*(1/1000)-1*(999/1000)}}}. This simplifies into *[invoke solve_equation "(x-1)*(1/1000)-1*(999/1000)"] So you would be payed $1,000.