For EF in triangle EFG, what is the corresponding segment in similar triangle HFG?
2 answers:
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There are ways of picking 2 of the 10 available positions for a 0. 8 positions remain.
There are ways of picking 3 of the 8 available positions for a 1. 5 positions remain, but we're filling all of them with 2s, and there's
way of doing that.
So we have
The last expression has a more compact form in terms of the so-called multinomial coefficient,