Equivalent Capital Pi Notation Expressions So I was working on a probability question and then this expression came up.
When I consulted the answers, I struggled to understand exactly how I would get from one expression to the other myself.

Substituting a constant such as
let $n=5$ makes it a bit clearer how they got from one expression to the other.
But is there a simple, yet general explanation of these expressions.
I am hoping the community could give some insight into how I should have approached this problem and similar ones in future.

Perhaps a picture will help.
Think about the set of points $(j,k)$ in the plane at which you are evaluating the fraction $(40-j)/(52-j)$ (which happens not to depend on $k$). You want to find the product of all the values. 
The points (with integer coordinates) will form a triangle. You can think of the product as finding the partial product over the rows first and multiplying, or over the columns first. One way is easier than the other.  
