Proof: Recursive Identity for Binomial Coefficients | Combinatorics

The binomial coefficient n choose k is equal to n-1 choose k + n-1 choose k-1, and we'll be proving this recursive formula for a binomial coefficient in today's combinatorics lesson!

This is the identity implicitly being used when we typically construct Pascal's triangle, and we can easily see why it's true by cleverly splitting the number of ways we can select k objects from n objects into two separate counts! Full details in the lesson!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+

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[jasonjones]

Thank you for taking the time to put this together. I really appreciate it. I won’t tell you how many times I watched it before k-1 clicked, but the 💡 moment was worth it!

[richardfrederick]

It works every time with any size set and any subset selected, but I still don't see why. I'm missing some basic, fundamental understanding.

[lonrdolo]

When you noticed that the letter h was too far from the rest of the word, you killed me. Nice video, thanks.

[filmgbg]

Fantastic explaination! Thank you so much for this video!

[om.a.n]

thank you for the video, but I have a question
Does the interval effect on this process? If yes explain how.

[mike_the_tutor]

Thanks for another great explanation! I've found videos on graphing sin^2 x and cos^2 x, using the power reducing formulas, but I have yet to find a video for graphing tan^2 x. I would love a step-by-step video for that. Just a suggestion though, no pressure. I'll be watching all your videos either way.

[Sam-AZ]

nice title : *wrath of math*

Thanks buddy. Good explaination

[maazshaikh]

Thank you so much. I was definitely searching for this kind of explanation. Keep it up!

[CesarAraujo-mu]

sorry but that's not the demonstration. It should be by operating one side till you get the original combinatory formula.

[nicolaevasiliu]

Great! Amazing! Incredible!
Thanx for sharing your knowledge in such a clear way!!!
Thank you! Gracias! Grazie!

[sainihith]

I understood the formula but it's not making any sense to me

[ammarhafiz]

Thank u sir ! U helped a lot.. much love from Malaysia ! 🇲🇾 ❤️

[vietlexuan]

Please make a video about maximum number of directed triangle in a complete directed graph

[davidplanet]

Isn’t this just Pascals’s triangle. T(n, k) = T(n-1, k) + T(n-1, k-1)

[manishsakariya]

I could have figured this out by myself but could not why!! 😐 Nice video thanks!

[YanivGorali]

Excellent and intuitive which is always great