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Source: HMMT November 2023 Guts Round Problem 8

Six standard fair six-sided dice are rolled and arranged in a row at random. Compute the expected number of dice showing the same number as the sixth die in the row.

I do not understand what the point of arranging the six dice at random in a line is. Wouldn't the problem be the same if the order was fixed to begin with and then each dice was rolled?

Benji
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    There's no particular meaning to the line. It's enough to imagine that one special die is selected uniformly at random and all the others are compared to that one (note: it's not clear to me whether or not the special die should be compared to itself, though of course the two computations just differ by $1$). – lulu Jan 03 '24 at 22:33
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    Certainly. Or even, "5 white dice and one red die are rolled. What is the expected number of dice showing the same number as the red die?" – mjqxxxx Jan 03 '24 at 22:33

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