# N Choose K Formula

N choose K is called so because there is (n/k) number of ways to choose k elements, irrespective of their order from a set of n elements.

To calculate the number of happenings of an event, N chooses K tool is used. This is also called the binomial coefficient.

The formula for N choose K is given as:

C(n, k)= n!/[k!(n-k)!]

Where,
n is the total numbers
k is the number of the selected item

### Solved Example

Question: In how many ways, it is possible to draw exactly 6 cards from a pack of 10 cards?

Solution:

From the question, it is clear that,
n = 10
k = 6

So the formula for n choose k is,

C(n, k)= n!/[k!(n-k)!]

Now,

$$\begin{array}{l}\textrm{C}(10, 6) =( _{6}^{10})=\frac{10!}{6!(10-6)!} =\frac{3628800}{17280}\end{array}$$

= 210

So, there are 210 ways of drawing 6 cards from a pack of 10.