Consider three positive integers x, y, and z that satisfy this equation:

comb(x,y)*comb(y,z) = 2*comb(x,z)

Does the above equation possess a finite number of solutions?

If so, determine all possible solutions of the above mentioned equation.

If not - then derive, with proof, the possible relationship between x, y, and z.

Note: comb(m,n) is the number of ways of choosing n unordered outcomes from m possibilities and defined as:

                m!
comb(m,n) = ---------
             n!(m-n)!

It is also known as binomial coefficient and read as "m choose n".