How Combinatorics used in data science
Read about the basics of Combinatorics for free in just 3 minutes
Combinatorics deals with combinations of objects from a finite set. To perform combinatorics, they have some restrictions (conditions) like avoiding repetition and order to get several favourable outcomes.
Types of Combinatorics :
Combinatorics has three parts, Namely
- Permutation
- Variations
- Combinations
I.Permutation :
- Permutation represents several different possible ways we can arrange a set of elements. Eg: a jigsaw puzzle.
- These elements can be in numbers, letters, etc.,
- Example: Consider three racers(drivers) namely Max, Bob, Ram if max won 1st place then Bob will be 2nd place and Ram will be 3rd place otherwise Bob won 3rd place and ram won 2nd price like this we have six unique ways those are referred as permutation.
Factorials :
n! => It returns the product of natural numbers from 1 to n
properties of factorials :
- A negative number doesn’t have a factorial.
- 0! = 1
Two factorials :
Example: Given two values n=7 and k=4
Variation with repetition :
The Total number of ways we can pick and arrange from the given set.
Variation without repetition :
In this method, we cannot use the same element twice.
Combinations :
- In this type, the number of different ways we pick certain elements from a set.
Variation :
- So, we have 6 permutations represented in a different variation, but not a different combination(Single Combination)
- Combination [C] can be calculated with the help of variance
The symmetry of Combination :
- This technique is applied to avoid calculating factorials of large numbers.
- Symmetry: To simplify calculations.
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