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?

lhyla02 Jun 18, 2020

#4**-1 **

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.

hugomimihu Jun 19, 2020

#5**+1 **

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

#6**0 **

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