In the lottery of a certain state, players pick six different integers between 1 an the order of the selection being irrelevant. The lottery commission then select of these numbers at random as the winning numbers. A player wins the grand of $1,200,000 if all six numbers that he has selected match the winning numbe wins the second and third prizes of $800 and $35 respectively, if exactly five an of his six selected numbers match the winning numbers. What is the expected of the amount a player wins in one game? Let x be the amount that a player wins in one game. To answer the question at we need to find: P(x=1,200,000) P(x= 800) P(x=35) P(x=0) We'll find these probabilities using combinations. P(x=1,200,000) = 1/49C6 = .000000072 P(x=800) = (6Cs)*(43CI)/49C6 =.000018 P(x=35) = (6C4)*(43C2)/ 49C6= .00097 P(x=0)= 1-.000000072 - .000018 - .00097 = .999011928