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Anonymous asked in Science & MathematicsMathematics · 1 month ago

# How much combinatorics do I need to know to learn probability & an introduction to statistics?

I am self-learning finite math via some videos from my online class and the narrator/teacher says that combinatorics (permutations & combinations) are foundational to learning the material in the following chapters -- such as probability & an introduction to statistics.

I have a basic understanding of combinatorics, but struggle with most of the word problems. I have pretty much given up at this point & want to move on to the other material. Will I be able to learn probability & stats as I am now, or will I end up totally lost?

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Combinatorics is important, but "foundational" might be overkill for a description. It IS foundational for doing a lot of problems, since problems often involve figuring how how many ways something can happen

I'm sure you know how to calculate permutations and combinations--that just takes simple formulas with a few factorials. The tricky part is recognizing how to apply those to to a problem. Here's an example, probably something you've seen:

How many ways can 8 people be arranged in a row if three of them must be together.

To do this, you need to recognize that the three form a unit, along with the other 5. So you have 6 units to deal with, and so the units can be arranged in 6! ways. Now you look at the three-person unit, which itself can be arranged in 3! ways, so you multiply by that, to get the final answer, 6!3!.

If you now have a probability problem to deal with about the 8 people, you might not get too far unless you first figure out the 6!3!.

So the combinatorics part is necessary to reach an understanding of the event space you are dealing with.

As others have said, yes, you will be better off if you improve your understanding of combinatorics.  Why don't you look at https://en.wikipedia.org/wiki/Stars_and_bars_(comb... to see something a bit more advanced, but surely not too advanced for you. It'll show you some clever ways to count things using tricks and the simple formulas. Memorize the formulas there if you can, though I admit I usually have to look them up to make sure I got them right.

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• You will not be able to grasp and understand prob and stat without mastering combinatorials - better to put the time in now to learn this material.

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• Once you move on to the various distributions (normal, binomial, poisson) they tend not get involved with combinatorics, so just move on and give it a go. But I would say it isn't promising if you are having problems with combo. My advice would be to look for other teaching material because they are not really that difficult. Sometimes the questions can be long and messy to solve but they shouldn't really be hard.

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