My Favorite Counting Technique includes ALL of the other Three!

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  • Опубликовано: 1 фев 2025

Комментарии • 14

  • @mulerseifu8824
    @mulerseifu8824 10 месяцев назад +3

    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🙏

  • @stanimir5F
    @stanimir5F Год назад +1

    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
      @DrSeanGroathouse  Год назад +2

      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
      @stanimir5F Год назад +1

      @@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
      @DrSeanGroathouse  Год назад +1

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

  • @davethesid8960
    @davethesid8960 Год 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.

  • @astro6774
    @astro6774 Год назад +1

    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
      @DrSeanGroathouse  Год назад +2

      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!

  • @eschudy
    @eschudy Год назад

    So cool!

  • @danielc.martin
    @danielc.martin Год назад

    Great!

  • @bigbigx2250
    @bigbigx2250 Год назад

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

    • @DrSeanGroathouse
      @DrSeanGroathouse  Год назад +3

      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
      @bigbigx2250 Год назад

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