The concept that, because Trig Palin has Down's Syndrome, this "proves" Sarah, not Bristol is his mother, keeps cropping up. I did some research on the actual numbers, and found out one or two surprising things. First, there is a slightly higher chance of Down's with very young mothers (15-19) than for mothers in their early twenties. The rate of Down's for women 15-19 years of age is 1/1250 while for women 20-24 years of age it's 1/1400. So while it's not a huge difference, it is interesting that the risk is higher, even by a little bit.
Here are the numbers I came up with. Right now in the US, we're sitting right around 4,000,000 births per year. According to the CDC for 2006, approximately 435,000 babies were born to women between 15-19. Based on this, taken with the 1/1250 ratio above, this gives us the information that approximately 350 Down's infants will be born to young women between 15 and 19 each year in the US. So while it's not a large number, it does occur often enough that it should not be considered so rare that it would be implausible.
And to a couple of people who have suggested to me that perhaps the Down's is also a fabrication: I doubt that. I'm certainly not an infant development specialist, but I have seen several photographs of Trig Palin in which I feel his Down's characteristics are very noticeable.