Binomial Coefficient Calculator

The binomial coefficient calculator determines the binomial coefficient C(n, k) of two positive integer numbers.

C(n, k) =  
n!
k! (n - k)!

How to Use the Binomial Coefficient Calculator?

  1. First, input the first (n) and second (k) integer numbers.
  2. Make sure that the first integer (n) value should be greater or equal to the second integer (k).
  3. After inputting the numbers, press the 'Calculate' button.
  4. As a result, the tool returns the binomial coefficient of given numbers.

How to Calculate?

The binomial coefficient is calculated using the following formula:

C(n, k) =  
n!
k! (n - k)!

Where,
n = First positive integer,
k = Second positive integer.

Let's take an example.

Example:

Suppose, you have a total of 9 books and you need to choose 5 of them. Calculate the binomial coefficient for this case.

Solution:

Here,
n = 9,
k = 5.

Let's put the above values in the formula.

C(n, k) =  
9!
5! (9 - 5)!
C(n, k) =  
9!
5! (4)!
C(n, k) =  
9 × 8 × 7 × 6 × 5 × 4!
5! × 4!
C(n, k) =  
9 × 8 × 7 × 6 × 5
5 × 4 × 3 × 2 × 1
C(n, k) =  
15120
120

C(n, k) = 126