Mathematics, 12.08.2020 08:01 Tamiahufflululu
The Happy Animals Kennel has $18$ cages in a row. They allocate these cages at random to $6$ dogs, $6$ cats, and $6$ pot-bellied pigs (with one animal per cage). All arrangements are equally likely. Let $A$ be the number of times in the row of cages that two animals of the same species are adjacent. For example, in the arrangement DCPCDPPPDCDPCDCCPD (where D=dog, C=cat, and P=pig), we have $A=3$. What is the expected value of $A$?
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The Happy Animals Kennel has $18$ cages in a row. They allocate these cages at random to $6$ dogs, $...
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