My Favorite Counting Technique includes ALL of the other Three!

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Multinomial Coefficients are powerful counting tools that include the other three fundamental counting tools: factorials, permutations, and combinations! In this video, we'll cover examples of using those three tools as well as how they all fit in the broader multinomial coefficients.

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25 янв 2024

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Комментарии : 14

@mulerseifu8824 3 месяца назад

I always struggled when it comes to counting things, i think it would be more saving if you made another video for us with a bunch of examples🙏

@danielc.martin1574 6 месяцев назад

Great!

@eschudy 6 месяцев назад

So cool!

@DrSeanGroathouse 6 месяцев назад

I'm glad you liked it!

@davethesid8960 5 месяцев назад

We used to call them permutations (factorials), combinations and variations (permutations). And the last is the same just with repetition, at least that's how I learnt it. It's called permutation with repetition. All of the above have counterparts with repetition.

@stanimir5F 6 месяцев назад

Very cool way of seeing at combinatorics indeed! I knew about the combinations with repetitions (what I called them) but haven't thought that it is the general case of all others. One question on the terms themselves. It could be caused by the difference in the languages but in Bulgarian: Factorial is the operation itself of multiplying all the numbers from 1 to N (N!) Permutation is an arrangement of ALL elements where the order DOES matter VARIATION is an arrangement of SOME elements where order DOES matter Combination is an arrangement of SOME elements where order DOESN'T matter Has it been changed or it has always been like you mentioned in the video in English?

@DrSeanGroathouse 6 месяцев назад

Thanks so much! I don't usually hear the permutation/variation distinction myself, but it seems to be common. In my classes growing up (and on my calculator) we used the permutation for both, like 5P3 (5 permute 3) to order 3 out of 5 distinct objects. But I think it's nice to have more specific terms for those!

@stanimir5F 6 месяцев назад

@@DrSeanGroathouseit might as well be a British vs American English thing. I just recently realized that the definitions for TrapezIUM and TrapezOID are not just different but exactly the opposite in meaning.

@DrSeanGroathouse 6 месяцев назад

@@stanimir5F I think you're right. And that trapezium/trapezoid difference is very confusing!

@astro6774 6 месяцев назад

despite getting a stem major I'd only heard of factorial (though I've heard permutations described similarly in a musical context). Very interesting

@DrSeanGroathouse 6 месяцев назад

Yeah, I think this is very common that these counting techniques are missed in the standard college math curriculum. I'm glad you liked it!

@bigbigx2250 6 месяцев назад

Do Americans just like not learn this? It was one of the first things I learnt in highschool combinatorics

@DrSeanGroathouse 6 месяцев назад

It seems to be pretty varied here. I remember learning permutations and combinations in high school. But I also know many students taking a probability class often haven't seen permutations and combinations, or at least not much. This video is a shorter version of what I would cover in the first week of that class to hopefully get everyone on the same page. I'm wondering, did you learn multinomial coefficients in high school as well? Or maybe you learned that technique but with a different name? I think in my high school we covered it as permutations with duplicate objects, like reordering AABBCCC. But we didn't learn a special name or notation for it.

@bigbigx2250 6 месяцев назад

@@DrSeanGroathouse it's as you said, I learnt the technique but without the name