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.
Thank you this was really helpful.
Very helpful, thanks!