Combination Calculator (C ⁿ_k)

What is Combination?

Combination is a content studied in combinatorial analysis, it describes the idea that a number n of elements can be arranged and rearranged in many different ways having repetitions between the ordered elements.

Use our combination calculator below. Enter values between 0 and 150 for n and k (remember: n >= k):

Combination Formula

The combination formula is represented by:

C_{n, k} = n! k!(n - k)!   ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ /

How to calculate Combination

Example:

n = 5
k = 3

To calculate the combination, it will be necessary to divide the factorial of the elements(n) by multiplying the factorial of the grouping(k) by the factorial obtained by subtracting the number of elements(n) minus the size of the grouping(k). To perform factorial division and multiplication, note that there are rules to be followed!
See the following example of the array calculation:

C_{5, 3} = 5! 3!(5 - 3)!   ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ = 5! 3!2! ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ = 120 12   ${\displaystyle \frac{}{}}$ $\dfrac {6!}{3!} =$ = 10

Difference between Simple Combination and Simple Arrangement

The simple combination and the arrangement are not the same thing, to be able to differentiate, just pay attention to whether the grouping of elements depends on ordering, if yes, it is an arrangement, if not, you must calculate a combination.

Reinforce your knowledge with the video below