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Die Order (Posted on 2013-01-04) Difficulty: 3 of 5
A single die is rolled four times.

What is the probability that the numbers that come up will be in ascending order (not necessarily strictly ascending, but never a lower number after a higher)?

Intended to be solved without a computer.

See The Solution Submitted by Charlie    
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Solution | Comment 1 of 7
There are 126 ways of doing this out of 6^4 which reduces to 7/72 ≈.0972222

126 = C(9,4)

The problem has the structure of tetrahedral numbers owing to the fact that we are rolling 4 dice.  I don't have time to explore where the 9 comes from.

  Posted by Jer on 2013-01-04 14:02:54
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