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)!]

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?


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)!]


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

= 210

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


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  1. Thank you this was really helpful.

  2. Very helpful, thanks!