In a state lottery, you must correctly select 5 numbers (in any order) out of 40 to win the top prize. 1. How many ways can 5 numbers be chosen from 40 numbers? 2. You purchase one lottery ticket. What is the probability that you will win the top prize? 3. If the order of the numbers mattered, will the probability of winning increase or decrease? Why?

Answer:In a state lottery, you must correctly select 5 numbers (in any order) out of 40 to win the top prize. 1. How many ways can 5 numbers be chosen from 40 numbers?40C5 = [tex]\frac{40!}{5!\times35!}[/tex] = 658008 ways.2. You purchase one lottery ticket. What is the probability that you will win the top prize?The answer is 5! ways or 120 ways.Hence, probability of winning top prize =[tex]\frac{120}{658008}[/tex] =0.0001 or 0.01 %3. The order of the numbers mattered, will the probability of winning increase or decrease? Why?The probability decreases.The probability of winning a game when order matters is always less than the probability of winning a game when order does not matter. This is because the permutation is always greater than the combination.