Subfactorial, a recursive approach

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In how many ways are there that we can do gift exchanges so that no one gets his/hers own gift back? Watch and find out this "derangement" concept! #derangement #ChristmasGift

Zero subfactorial

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blackpenredpen | 曹老師

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Small error: In the expression for !3 on the right side of board you have !(2-1) instead of !(3-2).

christophermusso

4! = number of ways to sit 4 people in 4 chairs
!4 = number of ways for them to do Christmas gift exchange so that no one gets his/her own gift back

blackpenredpen

1:37
"I think you guys know the answer, I don't..."
Shows the answer on his back
Not bad, bprp

alekseikhalin

Also, !0 = 1.
When there are no objects, doing nothing (the identity permutation) results in no object left in its original place!
This definition also satisfies the recursion.

And another useful way to write the recursion is
!(n+1) = n[!n + !(n–1)]

Fred

ffggddss

The really saddest story in math is that !1=0 😭😭😭😭💔

omarifady

But, the real question is what is

'i!' And '!i'
?

sarveshjadhav

now i have a fancy way of describing my life:

"subfactorial one"

pocarski

blackpenredpen: *asks complicated math question*
also blackpenredpen: *showes answer on back*

you're my favourit youtuber. I like your ways of doing things.

tsukibackup

yea, as if mathematicians have 3 different friends...
7:45 that is a much more realistic situation

AndDiracisHisProphet

Some friends were talking about gift giving
Naturally first think I thought of was this!

NonTwinBrothers

Wow you're really good at explaining! Loved it❤

gurpremsingh

Thank you so much for such a great gift. It helps me remember it. 😍

dwaraganathanrengasamy

Great video, didn t know about this derangement. The part about the “proof” of the recurring definition was kinda obscure to me ... I mean after thinking about it for a while I got convinced it worked but a better illustration (maybe a tree or whatever) would have been nice.
I know it s hard to present complex stuff clearly most of the times ... but hey you ve get two differently colored pen, we know you can do it :)
Thank you for teaching this new concept to me!

washizukanorico

but what is !0 ? Is it 0 because all 0 people get their own gift back or 1 because nobody gets their own gift back?

jumbochamploon

If you test this formula on normal factorial (using n!=n(n-1)!)
(n-1)((n-1)!+(n-2)!)
(n-1)(n-1)!+(n-1)(n-2)!
(n-1)(n-1)!+(n-1)!
(n-1+1)(n-1)!
n(n-1)!
n!

So this holds for factorial also. Interesting how much initial values change the result.

canaDavid