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Problem of the Week 1169

Roll the Dice

What is the expected number of distinct faces seen when throwing a 6-sided die n times?

Here is a related problem:

Suppose a standard die is rolled 6 times. Which is more likely: seeing 3 distinct faces or seeing 5 distinct faces?

Source: Julian Beasley; Matthew Conroy offers a nice download about dice problems.

© Copyright 2013 Stan Wagon. Reproduced with permission.

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25 October 2013