write applications of combinatorics on data science
Answers
Answer:
Gain a solid grasp of these fundamental concepts to improve your decision making process and drive your company forward.
We’ve recently talked about decision trees, game theory, and customer personas. For each topic, we’ve used examples that have a small number of cases so that we could show you something interesting, but manageable in size. Last week, we talked about how you can reduce the size of the problems you are trying to solve using clustering. This week, we will take one step even further back and talk about how to count the number of cases you have to start with.
To do this, we will talk about the mathematical field of combinatorics, in particular, permutations and combinations. A permutation counts the number outcomes where the order of what you are counting does matter. A combination, on the other hand, counts the number of outcomes where the order of what you are counting does not matter. Both permutations and combinations are further broken down to consider whether the options of what you are choosing from is allowed to be repeated, i.e., replaced in the set of available options after each choice, or not (you’ll see this concept referred to as both “repetition” and “replacement” — I’ll use “replacement” this week). We will talk about each scenario this week:
Permutations with replacement
Permutations without replacement
Combinations without replacement
Combinations with replacement
Step-by-step explanation:
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Permutations with Replacement
Back when we were talking about game theory, one of the scenarios we talked about was that your company (e.g., Doug’s Desserts) needs to make a decision as whether to raise your price, lower your price, or keep your price the same. Suppose you have 3 other competitors (let’s call them A, B, and C) that sell the same product as you, and they face the same three decisions. Also, you know from your past experience, that your company is the leader in the space and then each of the other companies always react to your pricing decisions in the same order, A then B and then C.
A permutation counts the number outcomes where the order of what you are counting does matter. A combination, on the other hand, counts the number of outcomes where the order of what you are counting does not matter.