What would happen to the possible variation in gametes if the number if chromosome pairs increased from two to three?

If each of the pairs of chromosomes was heterozygous (what gives you the highest potential number of different gametes), then the number of possible gametes increases from 4 to 8 for a diploid organism. To figure out how many are possible, raise the number of homologous chromsomes (2 for a diploid organism) to the power of the number of chromosomes. So if you have two different chromosomes (A and B), raise 2 to the 2nd power (or multiply 2 x 2) and you have 4. If you have chromosomes A, B, and C, then you have 2^3, or 2 x 2 x 2 = 8.

To show possible combinations, AaBb gives you AB, Ab, aB, or ab. AaBbCc gives possible gametes of ABC, ABc, AbC, Abc, aBC, aBc, abC, and abc.