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I have a set of feathers (a) and in that group there are (b) pigeon feathers.

How many ways can these feathers be arranged so that they are in a straight line so that no pigeon feathers are next to eachother?

Jun 18, 2020

#1
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How many are in these sets?

Or do you want it in terms of A and B?

Jun 18, 2020
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I was given no values so I need to present the answer with respect to A and B :)

lhyla02  Jun 18, 2020
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counting with restrictions... give me a bit.

Jun 19, 2020
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We can put the a feathers in a positions, so there are a! ways to place the a's, since aPa

there must be, at most, a+1 >= b, since there can't be more than one over a.

if you know what I mean.

If a is 2, b is 3,

babab

can't be anything else, so b can be at most 1 more than a.

Now.

b feathers can be placed at any of a+1 spots... _a_a_..._a_a_

so (a+1)P(b)

(a+1)! / (a+1-b)!

so we have this... $$(a+1)! * a~! \over (a+1-b)!$$

Please review this to see if I made any errors and if it is correft.

Jun 19, 2020
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That seems perfect to me!!

Thankyou so much for that, I was very stuck xD

Again thanks for taking the time to read over this question :)

lhyla02  Jun 19, 2020
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No problem.

If you need anything else feel free to ask or make a new thread!

Funny thing... I asked you to see if I was correct and I spelled correct wrong... i most definitely do not have correct spelling!

hugomimihu  Jun 19, 2020
edited by hugomimihu  Jun 19, 2020
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I did notice that! Can't criticise you for that though I'm no better myself xD

lhyla02  Jun 19, 2020