counting gene sequences

A friend of mine was writing a paper arguing against allowing patents for genetic sequences. In one case, a company patented a 15-gene sequence. He asked mt how many 100-gene genomes contain this sequence.

Now a gene can be one of 4 possibilities: A,T,C,G. So when i attempted to compute this counting problem, I thought for the specific 15-gene sequence, there were 86 possible starting points, and for any of the 86 genes not in the sequence there were 4 possible outcomes, so I came up with the computation:

86x4^85

Why is this computation wrong? explain and/or show your work

• What is 86x4^85? Is x multiplication symbol? – Zafer Sernikli Oct 25 '13 at 7:05

Your calculation is not wrong if you mean $86*4^{85}$ with "86x4^85".
Think that you're creating a 85 gene sequence. For any elements in the sequence, there are $4$ possibilities. You pick $1$ in $4$. You do this process for $85$ times. Then you have $4^85$ Now you're gonna add this 15 gene sequence somewhere between your sequence. You have 86 different spots to insert it, from the beginning to the end. Then $86*4^{85}$ is the true answer.