Part 3: Calculate Combinations and Permutations Problem 3 Problem Statement The number of ways of choosing & objects from a total of n objects without replacement when the order in which the objects are chosen does not matter is given by n! nok k! (n - k ) ! This is called a Combination and it gives the total number of combinations of & objects chosen from n objects. It the order in which the k objects are chosen matters, then we would use the formula n! n k (n -k)! This is called a Permutation and it gives the total number of permutations of & objects chosen from n objects. Use the formulas for Combinations and Permutations to calculate the probability of winning the lotteries described in the following questions. Give all answers to the questions as integers or fractions in lowest terms. Questions 1. Suppose a lottery was based on choosing 7 numbers from the integers 1 - 49 without repetition. If you choose the correct seven numbers, you win the $500,000 jackpot. What is the probability of choosing the winning numbers for the jackpot? a. How many ways are there to choose the numbers for this lottery if the order in which the numbers are chosen does not matter? b. How many ways are there to choose the numbers for this lottery if the order in which the numbers are chosen does matter? c. What is the probability of winning the jackpot if the order in which the numbers are chosen does not matter? d. What is the probability of winning the jackpot if the order in which the numbers are chosen does matter? 2. Use the information contained at the website for the Florida Lottery https:/flalottery.com/ to calculate the probability of winning the Mega Millions jackpot. Once on the website you should click on "Mega Millions" and then on "How to Play and How to Win" to get the information you need. a. How many ways are there to choose numbers for the Mega Millions lottery? b. What is the probability of winning the Mega Millions jackpot? 3. If a lottery game was based on choosing 7 numbers from the integers 1 - 50 without repetition, with another number chosen from the integers 1 - 28, what is the probability of choosing the winning numbers? a. How many ways are there to choose the numbers for this lottery? b. What is the probability of winning the jackpot? Example To win the Powerball jackpot you need to choose the correct five numbers from the integers 1 - 69 as well as pick the correct Powerball which is one number picked from the integers 1 - 26. The order in which you pick the numbers is not relevant, you just need to pick the correct five numbers in any order and the correct Powerball. Calculate the probability of winning the Powerball jackpot