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javamathstatistics
Jessica M.
Jessica M.

Reputation: 1459

Combinations function in Java

In one of the examples in my book it creates two methods. One called combinations and one called factorial. The body on the combinations method contains the following code

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

In an example of actually seeing how the math works out for this formula the textbook gives the following example. With n = 5 and k = 2. It gives the following steps and says you should get 10. I'm having difficulty understating the logic.

Does ! have a special meaning in this case? How does 5! = 120 and how does !2 x !3 = 2 x 6? 

C (n,k)  =     n! 
           _________
           k! x (n - k)! 



C (5,2)  =     5! 
           ___________
             2! x !3 


         =   120 
           _________
             2 x 6 

         =  10

Upvotes: 1

Views: 4276

Answers (3)

Michael
Michael

Reputation: 3332

! denotes a factorial. 

5! = 120

because 

5! = 5 * 4 * 3 * 2 * 1

and

2! x 3! = 2 * 6

because 

2! x 3! = (2 * 1) * (3 * 2 * 1)

Factorial

Upvotes: 1

Rohit Jain
Rohit Jain

Reputation: 213331

n! means factorial(n). It is equal to: -

n! = n * (n - 1) * (n - 2) * .... * 1

So, 

5! = 5 * 4 * 3 * 2 * 1 = 120

And !3 is rather a typo in your book. It doesn't represent a factorial

Upvotes: 1

Ted Hopp
Ted Hopp

Reputation: 234847

The ! (factorial) symbol means the product of all integers up to and including the number. So, for example:

5! = 5 * 4 * 3 * 2 * 1 = 120

This should help clarify what the factorial(int) method is doing.

By the way, if your book actually printed "!3" instead of "3!", it's a typo.

Upvotes: 0

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