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N Choose K Formula

N choose K is called so because there are (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 choose 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 :

\[\large _{n}C_{k}\equiv \binom{n}{k}\equiv \frac{n!}{k!(n-k)!}\]

Where,
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?

Solution:

From the question it is clear that,
n = 10
k = 5

So the formula for n choose k is,

$\binom{n}{k}=\frac{n!}{k!(n-k)!}$

$\binom{10}{6}=\frac{10!}{6!(10-6)!}$

$=\frac{3628800}{17280}$

= 210

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

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