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CCC comments on Welcome to Less Wrong! (July 2012) - Less Wrong
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Ah, I see. You'll be glad to know that there are often ways to shortcut the counting process. The specifics often depend on the problem at hand, but there are a few general principles that can be applied; if you give an example, I'll have a try at solving it.
It is, indeed.
In fact, many if not most concepts in probability theory deal with various ways of avoiding the counting process. It gets way too expensive when you start handling billions of combinations, and downright impossible when you deal with continuous values.
asdfjkl; I wrote out all the pairs. -_- Can't trust these problems otherwise! Grumble.
"You are never too cool to draw a picture" -- or make a list or a chart. This particular problem is well served by a six-by-six grid.
Dice are okay; it's the problems with cards that get toooo huge. :)