Our previous example shows a dihybrid cross, where we observe the pairings of genes that underlie two different traits.  What would the predicted outcome of a cross look like with three genes (Q/q; S/s; T/t)?  I wrote a computer program to determine the result:

OK, big deal, you say.  A few minutes’ work with a pencil and paper could produce this chart.  Well, then let’s try four different genes (Q/q; S/s; T/t; V/v):

A bit more difficult to do on  paper, wouldn't you agree?

I would show ten genes, but the program would need to run for many hours to produce the gigabyte-sized result.  Plus, it might crash your computer to download the massive thing. 

Now, let’s get back to nature: what really happens during a cross?  Plants like orchids can have many thousands of genes.  Humans have around 30,000 genes.  So in a human cross, you’d have 2^30,000 allele combinations in each parent, making the total number of potential combinations in a cross 2^30,000 x 2^30,000.  Try writing all those genotypes on a piece of paper!