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 happening of an event, N chooses K tool is used. N is the sum of data and K is the number that we chose from the sum of data.

The formula for N choose K formula is :

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

n is the total number
k is the number of selected item

Solved Examples

Question 1: How many ways 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)!] \(_{10}^{6}\textrm{C}=\frac{10!}{6!(10-6)!} =\frac{3628800}{17280}\)

= 210

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


  1. Thank you this was really helpful.

  2. Very helpful, thanks!

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