Constant Rule? Why do we have to divide by 6?
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[Originally posted in Discussions]
So when Professor Loh said that you have to divide by half because you would've counted every intersection twice with 6 times 5 using the rule 6 choose 2, does that mean you have to divide by 2 after multiplying for every single question of this type?
Thanks for asking! It's not always true that you must divide by 2 to eliminate the copies, because sometimes you divide by other numbers. You can look at the long response to your earlier question. The number of triangles was
and we divided by 3!, which equals 6, because there are 6 copies of each way to make a triangle. These are the six ways to make a triangle with the red line, dark green line, and yellow line:
The number of copies per way depends on the question.
I hope this helps! Good luck on the rest of the course, and please ask if you have any more questions!
The Daily Challenge Team