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Thank you gAr and Elaine these are beautiful solutions. I understand only the one with the double recurrence. Thanks for the explanation, anonymnistify.
Hi Bobby,
Actually, the derivation ...
Anybody,
How did gAr get that result?
Is there something like "combinatorics for dummies" on the web?
I did discover something exciting (to me, but seems trivial now). Distributing n snails among k people (where all the snails are the same):
Since we start with 1 for each person, it's n = 20 - 4 = 16
Any help on this notation gAr used would be appreciated.
Thanks. I looked up the "absorbing" Markov chains. It turns out that it does not matter how many absorbing states there are. The answer only depends on the fundamental matrix Q.
Fascinating that matrices (n-by-n ones anyway) obey the rules of algebra, like:
I - Q (to the n+1)
I + Q + Q² + Q³ + ... + Q (to the n) = -------------------------
I - Q
Is that correct?
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