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
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
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
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
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 !!!!