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Ok I am wondering if anyone out there can help me.
I want to find a formula, call it ƒ(x,y), where x and y are whole numbers and x,y > 0.
ƒ(x|y=1) means ƒ(x), given y=1.
After some lengthy calculations I know the following:and thus, seeing the pattern, I can conceive the following:Code:ƒ(x|y=1) = x^-0 { + 0 } ƒ(x|y=2) = x^-1 { + 1 } ƒ(x|y=3) = x^-2 [ (x-1) { + 2 } + x ] ƒ(x|y=4) = x^-3 { (x-1) [ (x-2) { + 3 } + 2x ] + x^2 } ƒ(x|y=5) = x^-4 [ (x-1) { (x-2) [ (x-3) { + 4 } + 3x ] + 2x^2 } + x^3 ]
ƒ(x|y=6) = x^-5 { (x-1) [ (x-2) { (x-3) [ (x-4) { + 5 } + 4x ] + 3x^2 } + 2x^3 ] + x^4 }
You may also be able to see the pattern here. So as there is a pattern, I think ƒ(x,y) exists. Any help?
Btw, this is to do with the chance of a number showing up at least once on an x sided dice with y dice. Or more to my intention, to work out ƒ(x|y=365), the chance of two people having the same birthday with x people in the room.
I got something, haven't checked it fully though. See the attachment
Ciao
Stonehambey