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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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Answer | Comment 2 of 7 |
There are 6^4 = 1296 permutations with repetition possible.
Though not specifically mentioned but implied, at least one ascent is required in order for the numbers to be considered ascending. In this interpretation, there is a 120/1296 = 5/54 probability that the numbers will be in ascending order with at least one ascent.

There is a 126/1296 = 7/72 probability that in the numbers will appear with no lower number after a higher. There is a 5/432 probability that the numbers will be in strict ascending order. And, there is a 1/432 probability the ascending order will be strictly consecutive.
  Posted by Dej Mar on 2013-01-04 16:03:51
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