I was analyzing the following code concerning Lottery Odds and I have 2 questions:

• why do we need to set lotteryOdds' value to 1 first (also, is it a usual situation in calculations of this type?)

• I know the formula used for counting the odds (n*(n-1)...(n-k 1)/(1*2...*k), but if someone explained me how it works in accordance to repeating the "for" loop, I'd appreciate.

  import java.util.Scanner;
  
    public class LotteryOdds {
  
  
        public static void main(String[] args) {
  
        Scanner in = new Scanner(System.in);
  
        System.out.println(" How many numbers do you need to draw? ");
        int k = in.nextInt();
  
        System.out.println(" what is the highest numbers you can do draw? ");
        int n = in.nextInt();
  
        int lotteryOdds = 1;
  
        for (int i = 1; i <= k; i  ) {
            lotteryOdds = lotteryOdds * (n - i   1) / i;
  
            System.out.println("Your odds are 1 in "   lotteryOdds   " . Good luck!");
        }
  
    }
  

  }

CodePudding user response：

The lotteryOdds variable needs to be 1, because if you do 0 * something you will always get 0, so the program will always return 0. As for the loop, lets change the values and go trough the loop: First iteration:

lotteryOdds = 1 * (n - 1 1) / 1 = n / 1

Second iteration:

lotteryOdds = n * ((n - 2 1) / 2) = (n / 1) * ((n - 1) / 2) = n * ((n - 1) / 2) = ((n * (n - 1)) / (1 * 2)

Etc. So when you generalize it you get: (n * (n - 1)...(n - k 1) / (1 * 2 ... * k) just like in the formula above.