Arrangements and Derangements with Repetition

A very interesting topic in discrete math, combinatorics,

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blackpenredpen | 曹老師

[ethancheung]

aren't you double counted? the first "false" derangement !5 (p1urple -> ***p1**) contains (p2**p1**), also the second "false" derangement !5 (purp2le -> p2****) also contains (p2**p1**). so I think you should not -!4 but +!4 to make up the count.

[rksmehul]

Now do derangement of
"Mississippi"

[shubham]

Are these topics related to Permutations and Combinations? Thanks I was eagerly waiting for the videos from this topic.

[parasjain]

Great Video . The only video in the internet with "derangement with repetition"

[Electroneer]

Why am I watching this at 3 am? Math is too interesting sometimes.

[ujjwalchauhan]

Thanks, that is really helpful for jee.

[snatcc]

I can’t wait for t”the color purple” movie”, so balck

[protessional]

Hi, I'm a high school student and I've stumbled across an interesting limit that I've tested and it seems to converge to a complex number, but I cannot see what value it approaches. I will explain the limit now: Suppose f(n, m) := ln(ln(ln...(ln(m))...) where there are n natural logs (f(0, m)=m. f(1, m)= ln(m)). the limit is then lim n -> ∞ f(n, n).Could you explain this? Edit: Researched this today and worked out that it goes to
-W(-1) or if you write -W(-1) as a+bi another fixed point is a-bi.

[ethancheung]

I have encountered a question if you could solve. Given a bezier curve in parametric form B(t), t0 and L, find t1 such that arc length from B(t0) to B(t1) equals L.

[angelmendez-rivera]

Ooh. Nice. Can you solve the equation Sqrt(x^2 + y^2)*e^(1 - y) = 1 in terms of y? You are allowed to use the Lambert-W function.

[arandompersononyoutube]

Do arrangements and dearrangements of blackpenredpen.

[PigZombiePacifico]

if n is the number of letters and m is number of letters that repeat, got that the number of derangements is going to be:
(!n-(Σ(mCk)*!(n-k)))/m!
Where the sum goes from k=1 to m.
Is that right?

[aswinibanerjee]

So in general derangement of n aliments in which m aliments are same the formula is
#=[!n-m×!(n-1)-!(n-m)]/m!

[ErickSousa-lxqr]

So the formula of derrangements when there are 2 repeated elements is
[!n - 2 × !(n-1) - !(n-2) ] / 2!, right?

[samokoribanic]

Can you try to solve this question. We have table where sides are a and b long. Question is how many combinations we have to color full table with 4 colors such that no 2 same colored squares will be neighbours... I cant figure that out..

[rajatkhandelwal]

Sir you have never make video on vectors and 3d like topics plz make interesting videos too on these topics

[waynemv]

@blackpenredpen, would you please follow up with a counting of the derangements of the letters in "derangement"?

[andrescamilohernandezruiz]

Can you solve this integral? Integrate (1+x^4)^(1/2) dx

[Kitulous]

I love purple color!.... and also yellow. But yellow pen wouldn't be too visible on a white board. Can I congratulate you with using a new pen color?

[sword]

what if you want to rearrange the letters aabbcc so that same letters never come together ?