Find all ways of grouping five multiplied numbers

I am working through Israel Gelfand's book "Algebra" and am stuck on the following problem:

*Find all possible ways to put parentheses in the product 2*3*4*5*6 (not changing the order of factors). Try to invent a systematic way of searching so as not to forget any possibilities.*

I calculated 16 possibilities by rote before giving up (there may be more), and the only thing I accomplished in the way of "systematic" was stating that in any sequence of five numbers there are four operations to be performed. Perhaps it's the late hour, but I can't get beyond this. Any suggestions?

Thanks!

Re: Find all ways of grouping five multiplied numbers

I think you are correct in this one, I am also kind of stuck with this problem in Gelfand's book and I think I counted every possibility for 2*3*4*5*6 and I always get 16 an result which can also be calculated by 2^{n-1}. So thank you for helping.