Shouldn't the Hofmann product be preferred in this elimination? Shouldn't the exocyclic alkene (Hofmann) be the major product? The base is $\ce{t-BuO-}$ (tertiary butoxide ion), which is pretty bulky. I think the Saytzeff product should be the minor product. 

Also, the solution says "E2, some E1". It's a 3° alkyl halide (more sterically hindered than 1° and 2°), so shouldn't it undergo E1 elimination?
Yup, $\ce{t-BuO-}$ is a bulky base.

But is it bulky enough that it can't even abstract a hydrogen from the ring? Nope.

Take a look at this picture of a $\ce{t-BuO-}$ molecules approaching the hydrogen of 1-bromo-1-methyl-cyclopentane.



Does that $\ce{t-BuO-}$ look like it's struggling to pull that hydrogen out? Definitely not. It's doing what it does with ease.