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> (1) Given 8 red balls and 7 blue balls arranged randomly in a sequential fashion, what is the average number of pairs of distinct adjacent balls ?
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> For example the sequence $\mathbf{RBR}RRRRR\mathbf{RB}BBBBB$ would contribute 3 pairs, $\mathbf{RB}$ in slot $(1,2)$ , $\mathbf{BR}$ in slot $(2,3)$ and $\mathbf{RB}$ in slot $(9,10)$
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> 2) Same question but with 6 red balls, 5 blue balls, 4 white balls
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* My attempt for (1) is to consider the first 2 slots, and state that these will form a pair if it is either BR or RB, so that the probability of the first 2 slots being a pair is:
$$ \frac {7} {7+8} \* \frac {8} {7+7} + \frac {8} {7+8} \* \frac {7} {7+7} $$

but then for slots (2,3) , given that there is no replacement and overlap with slot (2) for slots (1,2) , i am not sure ...

* I guess if I can manage (1) then (2) is similar ?