Farkle formulas using MathML

Rules of Farkle

Probability of Farkling with six dice:
To Farkle with six dice, you have to not roll any 1's or 5's. (for this problem, let's choose the dice in order) So, you have to choose 6 dice from the set 2346 . However, you can't get more than three of any of these elements, and you can't get three pairs either. So this leaves us with choosing 2, 2, 1, 1 of the set 2346 . The number of ways to do this is just the number of ways of first choosing which numbers to choose two of ( 4 2 42 6 ) and then ordering these ( 6 2 2 180 6 ! 2 ! 2 ! ) So, the total number of ways to do this is 6 180 1080 , and the total number of ways to roll 6 dice is 6 6 46656 , so the total probability is 1080 46656 1080 46656 .0231481 , or about 2 percent.

Wow, it says in the MathML spec that

As a consequence, raw MathML markup is not primarily intended for direct use by authors. While MathML is human-readable, which helps a lot in debugging it, in all but the simplest cases it is too verbose and error-prone for hand generation.
and they're right. Coding this stuff up by hand is a pretty big pain.

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