[Discrete Mathematics] Derangements

We talk about derangements.

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In this video we look at derangements. That is, the number of ways we can return items so that nobody gets their own item back.

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[abdullah-ayy]

I don't get why would anyone dislike this video?
He's better than most of my proffs

[yaweli]

Wow, good job. I have struggling with combinatorics, cuz I missed tons of classes. With you, i will catch up. Thanks.

[proggenius]

It's cool to learn from someone who knows what he's teaching inside out!

[GerardFunClub]

I'm majoring in statistics and this video has helped me a lot, thank you, sir!

[antmanistheman]

I'm a bit confused it seems that if you multiplied the total number of derangements by the total number of ways in which to arrange student their would be more way to derange them then arrange them I don't think youre wrong I just know theres something I don't understand. This question pertains to the problem about 17:00 minutes in concerning the desks.

[bradimi]

For dn = n!/e, is it true that if n is even, then you would always take the ceiling of n!/e, and if n is odd, then you would always take the floor of n!/e?

[darianharrison]

Thank you very much for these coursers, they are very helpful

[captainfoodman]

great video!!
but I didn't understand the Ms.pezzulo question. where the question states she teaches both classes. so in the first class the no of ways she can assign desks to 12 students so that they don't get their own is D12. but then for the second class, all these new arrangements must also be avoided. so during the second class it will be (12!-D12). then shouldn't we multiply D12(12!-D12) for the final answer. 

and this question didn't tell us to do two different things such as "assigning to 12 students and then rearranging them" right?? it goes like 'how many ways can she assign it to them such that they don't get their own desks.'

And if I'm wrong, then why did they give the information that she teaches two classes one after the other.

[Indhu]

Thank you so much for uploading all these awesome clearly explained videos!!!I'm preparing for an exam tmr and you have helped me more than my prof 😊😊😊😊😊

[davemartin]

At time 4:19, you say S4 is uncounted due to multiplication by 0!. However, isn't 0! = 1! = 1?

[jasonspence]

Huh... that's clever to choose 6 of the 12 to do the derangement... I instead calculated it out as inclusion-exclusion for exactly 6 of the criteria (i.e. E6 = 12![ 1/6! - nCr(7, 1)/7! + nCr(8, 2)/8! - ... + nCr(12, 6)/12! ] ) and it comes to the same number!

[burninredcrab]

When you factored out n! at 10:30, I think the last term should just be 1/1 or 1. Not 1/n! since you factored it out.

[Selim_Hasan_Raj]

these videos are awesome. thank you so much.

[adityasinghverma]

Thanks a ton man!! :) You're awesome!

[manishvarma]

I was pretty surprised when you wrote 10, 11, 12 in hexadecimal 🤣🤣🤣

[CollectorWorth]

16:35 actually it's the name of my band

[kshitijingle]

can u make a video for this:-
Dn= nCn-r * Dr

[sambit]

how to solve dearangement problem having identical object... such as dearangement of "varoon"

[Pride]

Why does S0 need to be included for this example...?

[souravganguly]

e^x =1+x+1/(2!)x^2+1/(3!)x^3.... if x=1; e=1+1/(1!)+1/(2!)+... So how come dn=n!/e?