CORRECTION AT 13:51 - I accidentally added 4 twice. Sorry about that. n + r - 1 is 8 + 4 -1 = 11. It should be 11C4 = 330. Thanks @Sport Master for pointing this out.
Seven people in a room. How many handshakes are made? 7! / 2!5! person A handshakes the others and go out the room (6) person B handshakes the others and go out the room (6+5) At the end we have 6 + 5 + 4 + 3 + 2 + 1. A triangular number! isn't that beautiful, considering that factorials are the same but with multiplication? In fact, 6! is 6 * 5 * 4 * 3 * 2 * 1 and sixth triangular number is 6 + 5 + ... + 1. this problem is a combination poblem. But it's a permutation problem as well. It's a permutation of two groups of letters: YYNNNNN And combination with repetition is a permutation of bars and stars. Everything is a permutation! Combinatorics is beautiful
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CORRECTION AT 13:51 - I accidentally added 4 twice. Sorry about that. n + r - 1 is 8 + 4 -1 = 11. It should be 11C4 = 330.
Thanks @Sport Master for pointing this out.
Seven people in a room. How many handshakes are made? 7! / 2!5!
person A handshakes the others and go out the room (6)
person B handshakes the others and go out the room (6+5)
At the end we have 6 + 5 + 4 + 3 + 2 + 1. A triangular number! isn't that beautiful, considering that factorials are the same but with multiplication? In fact, 6! is 6 * 5 * 4 * 3 * 2 * 1 and sixth triangular number is 6 + 5 + ... + 1.
this problem is a combination poblem. But it's a permutation problem as well. It's a permutation of two groups of letters: YYNNNNN
And combination with repetition is a permutation of bars and stars. Everything is a permutation! Combinatorics is beautiful
Just sees you 2 years old video power set very help full thx
Form India
Thank you for watching!
I have a test tomorrow and this helped so much!
I like your videos ❤ from india ❤
Thank you!
Mistake in the final example Sir. Should be 11C4 I think. Great video!
Drats, can't believe I missed that in editing! Thanks!
Your videos, including the ones on set equality proofs, are excellent! Very underrated channel. Thank you and hope you get more recognition/subs!
combinations always confused me because "order does not matter" -- but for combination locks order DOES matter
Yeah they should definitely be called permutation locks! Oh well.
@@WrathofMath HAHA such a nerdy joke but I like it
You look a lot like Freddie Highmore!
What calculator program is that? Mine is not as user friendly