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.

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