Example: Permutations of n people in r seats in Java

// Permutations of n people in r seats
import java.util.Scanner;

// Main class containing the entry point of the program
public class Main {

    // Method to calculate factorial of a number
    public static long factorial(int num) {
        if (num < 0) {
            return 0; // Factorial not defined for negative numbers
        }
        long result = 1;
        for (int i = 1; i <= num; i++) {
            result *= i;
        }
        return result;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        // Step 1: Get input for n (number of people)
        System.out.print("Enter the total number of people (n): ");
        int n = scanner.nextInt();

        // Step 2: Get input for r (number of seats)
        System.out.print("Enter the number of seats available (r): ");
        int r = scanner.nextInt();

        // Step 3: Validate inputs
        if (n < 0 || r < 0) {
            System.out.println("Number of people and seats cannot be negative.");
        } else if (r > n) {
            System.out.println("Number of seats cannot be greater than the number of people.");
        } else {
            // Step 4: Calculate n!
            long nFactorial = factorial(n);

            // Step 5: Calculate (n-r)!
            long nMinusRFactorial = factorial(n - r);

            // Step 6: Calculate permutations P(n, r) = n! / (n-r)!
            long permutations = nFactorial / nMinusRFactorial;

            // Step 7: Display the result
            System.out.println("The number of permutations for " + n + " people in " + r + " seats is: " + permutations);
        }

        scanner.close();
    }
}