Question

I’m studying the code below in my textbook. It uses the combinations method and the factorial method to calculate the possible outcomes given n and k. My question is with the factorial method specifically the content in the for loop.

I understand everything else about the program but I don’t understand the code i <=n in the for loop in the factorial method. What other part of the program is n referred to? I’m just not sure about the rationale behind i <= n or how the programmer comes up with that.

import acm.program.*;

public class combinations extends ConsoleProgram {
    public void run(){
        int n = readInt("Enter the number of objects in the set (n): ");
        int k = readInt("Enter the number to be chosen (k): ");
        println("C (" + n + ", " + k + ") = " + combinations (n, k) );

    }

    private int combinations (int n, int k){
        return factorial (n) / (factorial (k) * factorial (n-k));

    }


    private int factorial (int n){
        int result = 1; 

        for (int i = 1; i <= n; i++){
            result *= i;

        }
        return result;

    }

}

Answer 1

n is a parameter of the method: because the method is declared as int factorial(int n), you invoke it as (for example) factorial(5) to get the local variable n set to 5. (In formal terms, n is the parameter and 5 is the argument, though usually people don’t bother to distinguish those two terms.)