Project 2: Powerball (or, Why Throwing Money at the Lottery Is a Bad Idea)
Background Information
This assignment involves simulating a lottery drawing. In this type of lottery game, the player picks a set of numbers. A random drawing of numbers is then made, and the player wins if his/her chosen numbers match the drawn numbers (disregarding the order of the numbers).
More specifically, a player picks k distinct numbers between 1 and n (inclusive), as well as one bonus number between 1 and m (inclusive). "Distinct" means that none of the first k numbers may be repeated. However, the bonus number may or may not coincide with one of the k distinct numbers. The k distinct numbers as well as the bonus number must match the drawn values for the player to win the jackpot.
The TN Lottery's Powerball game is a good example of this type of lottery. In this game, a player picks five numbers between 1 and 59, inclusive, and one "Powerball number" between 1 and 35, inclusive. Here, the number of possible lottery tickets is:
{(59 x 58 x 57 x 56 x 55) / (5 x 4 x 3 x 2 x 1)} x 35 = 175,223,510
A single ticket's chance of winning the jackpot is then 1/175,223,510, which is about 0.0000000057. To put that probability in perspective, suppose you were to sell your Harbor Town mansion for $600,000 and use the proceeds to buy Powerball tickets. Since tickets cost $2 each, $600,000 will buy you 300,000 tickets. Even with that many, your chance of winning the jackpot is still a miserably low 0.0017 - less than two tenths of one percent. Makes you think twice about buying that lottery ticket, doesn't it?
In general, for this type of lottery drawing the number of possible tickets is:
[{n x (n - 1) x (n - 2) x ... x(n - k + 1)}/ {k x (k - 1) x (k - 2) x ... x 3 x 2 x 1}] x m
The Assignment
Write a Java program to simulate a lottery drawing. Your program should allow the user to enter values for k, n, and m above. Then, ask the user to enter the numbers that s/he wishes to play (this is your program's equivalent of "buying" a lottery ticket). Store the k distinct numbers into an array, but keep the bonus number separate.
The program should compute and display the probability of winning the jackpot for the selected game. Then, it should randomly "draw" the winning numbers and determine if the user-entered numbers match. Keep in mind that the matching for the k distinct values should disregard the order of the numbers. The winning numbers should be shown, along with an appropriate message indicating whether or not the user won the jackpot. Allow the user to play as many games as s/he wants.
Error Checking
Implement error checking on all user inputs, to the extent we've discussed it in class (don't worry about data type mismatches). Error checking should repeatedly prompt for the input until the user enters a valid value. For example, the user should not be able to enter negative inputs. The user input should also be checked to see that it matches the entered values for n and m - for example, in a game where n = 59, the user should not be able to pick 60 for his/her ticket. Also make sure that you're checking for distinct inputs when the player chooses numbers - a player shouldn't be able to pick the same number more than once (with the exception of the bonus number).
Code Organization
Your program should use methods to break the code down into manageable chunks. At minimum, include the following methods (although you are welcome to add more if you want).
// Returns the probability of winning the jackpot in a lottery drawing with the
// specified parameters.
public static double jackpotChance(int k, int n, int m)
// Allows the user to enter k distinct integers between 1 and n. Must include
// error checking to ensure that each entered number is within the valid range and
// does not coincide with any previously entered number. Returns an array of
// the entered numbers.
public static int[] enterNumbers(int k, int n)
// Makes the computer draw k distinct random integers between 1 and n. Returns an // array of the drawn numbers.
public static int[] drawNumbers(int k, int n)
// Returns whether the two arrays a and b contain the same elements, without
// regard to order. For example, if a = {1, 4, 3, 2} and b = {1, 2, 3, 4},
// this method should return true.
public static boolean containSameElements(int[] a, int[] b)