How many arrangements can you make by selecting 3 items from a set of 20? I got $$\frac{20!}{17!3!} = 1140$$
but my textbook says the answer is 570. Also I'm not really sure how using the word arrangements translates to unordered combination. My first instinct was to try permutations. We could first select 3 and then arrange those $3$ in $3!$ ways. 

I agree with your observations.
I would use permutations, $^{20}P_3 = 20\times19\times18$
and even supposing that combinations are used, ${20\choose 3} = 1140$
