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?
How many are in these sets?
Or do you want it in terms of A and B?
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,
can't be anything else, so b can be at most 1 more than a.
b feathers can be placed at any of a+1 spots... _a_a_..._a_a_
(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.
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 :)