N Choose K doesn't make sense?

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

:\(C(n, k)= n!/[k!(n-k)!] \)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
N = 6

So the formula for n choose k is,\(C(n, k)= n!/[k!(n-k)!] 610C=10!6!(10−6)!=362880017280 \)= 210

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

This formula and topic is very useful in solving various types of problems I recommend that you you practice this topic until you feel like you can solve and N choose K question.

Here to help

:D

Anything choose 0 is 1, Anything choose 1 is the number i.e. 1 choose 1 is 1, 2 choose 1 is 2, 3 choose 1 is 3 and so on. You can't use negative numbers is combinatorics.

Here's proof of LuckyDucky's answer  of 0 choose 0

C(0,0)  =

      0!                    1                1

__________  =   _____   =  _____   =  1

(0 - 0)! * 0!           0! * 0!        1  * 1

But....think about this...we have no objects and we want to choose none of them

There's only one way to do this.....forget about it   !!!!