I think my previous answer was wrong, let me do more research and then I'll post an answer unless somebody gets it first.
Hello, math sucks!
I have an approach to this problem.
But I have no proof of my theory . . .
A die is tossed 6 times. What is the probability that on each toss,
the number shown is less than or equal to the previous tosses?
Consider rolling two times.
The outcomes are:
. .
. .
Out of the outcomes,
. . a triangular number, are desirable.
Roll three times. .There are: . outcomes.
The outcomes will be displayed in a 6×6×6 cube.
Picture a plane "bisecting" the cube through two opposite vertices.
The desirable outcomes are in the the "larger half".
This is a tetradedon with sides of 6.
It contains: outcomes.
Roll four times. .There are: . outcomes.
The ouctomes are displayed in a 6×6×6×6 hypercube.
The "larger half" contains: . outcomes.
Let's skip to six rolls. .There are: . outcomes.
The outcomes are in a 6×6×6×6×6×6 hypercube.
The "larger half" contains: . outcomes.
Therefore: .