Question

What’s the easiest way I’d work out the total possible combinations of a method? Here is an example class of what I’m trying to work out;

class Combinations {

    public void generate()
    {
        final int TOTAL_A = 10;
        final int TOTAL_B = 21; // TOTAL_B is used twice
        final int TOTAL_C = 17;
        final int TOTAL_Z = 20;
        int count = 0;
        for (int a = 0; a < TOTAL_A; a++)
        {
            for (int b = 0; b < TOTAL_B; b++)
            {
                for (int b_two = 0; b_two < TOTAL_B; b_two++)
                {
                    for (int c = 0; c < TOTAL_C; c++)
                    {
                        for (int one = 0; one < TOTAL_Z; one++)
                            for (int two = one + 1; two < TOTAL_Z; two++)
                                for (int three = two + 1; three < TOTAL_Z; three++)
                                    for (int four = three + 1; four < TOTAL_Z; four++)
                                        for (int five = four + 1; five < TOTAL_Z; five++)
                                            count++;
                    }
                }
            }
        }
        System.out.println("Total combinations: " + count);
    }

}

What would be the way to figure out what “count” would be without having to actually do the loops?

Answer 1

|A| * (|B| choose 2) * |C| * (|Z| choose 5) = 553,492,800

Or if you want to choose from two different pools B1 and B2 that have the same size:

|A| * |B1| * |B2| * |C| * (|Z| choose 5) = 1,162,334,880

where n choose k is defined as follows:

n!/(k!*(n-k)!)