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Probability Expected Value Combinatorics

Guide: Optiver Interview Questions: The Process, the Games and How to Prepare

A fair six-sided die is rolled 10 times.

Let

$N_i$

be the number of times face $i$ appears, for

$i=1,\ldots,6.$

Find

$E[N_1N_2N_3N_4N_5N_6].$

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Product of Face Counts in Ten Die Rolls

Product of Face Counts in Ten Die Rolls