We might have heard about Factorials right from our childhood and also one of the best example learning any programming language.
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positiveintegers less than or equal to n.
For example,
5 ! = 5 * 4 * 3 * 2 * 1 = 120
4! = 4 * 3 * 2 * 1 = 24
3! = 3 * 2 * 1 = 6
The value of 0! is 1.
In mathematics, a combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.
For example:
How many possible ways can we pick 2 out of 5 numbers? And put them from low to high.
Arranging the possibilities from low to high, If you see the below image we have five cross marks out of two are gray and remaining are blue, as per the question what is the probability of picking 2 out of 5.
The numbers you see like 12,13,14….. 12 means if we arrange the gray color on the first and second place than 1 and 2 (12),If we arrange the gray color at position 1 and 3 then it is 13, same if we arrange at the position 4 and 5 than 45
So they are total 10 possibilities of picking the 2 out of 5 (if you count the total from 12,13…. To 45)
As this is just 2 out of 5, we can draw like above and can decide, what happens if we have large numbers?We always will have the formulas to calculate this kind of problems, in our case combinations.
Where
N = number of observations
r = number of different ones
We know how to calculate factorial,let’s solve our problem, with our formula.
N = 5,r=2
So there is 10 possibilities of picking two out of 5.
Data and Machine by viswateja 