Frequency of nucleotide sequences of specific length in DNA

1. How frequently would you find the nucleotide sequence GGATATCCGC (5' to 3' direction) by chance in a DNA molecule?
2. On average, how many times do you expect to find a specific 20 nucleotide sequence in a genome with a total size of 4 x 109 base pairs?

Since that probability of finding each base pair in its given position is 1 in 4, thus the total probability of finding that particular sequence would be $$0.25^{10}$$

But how do I approach the second problem?

TIA

• While the 'background' of this question is biology, it's actually a pure combinatorics & statistics question. I'd recommend asking this on a different SE site. – Nicolai Mar 11 at 16:12
• Apply the frequency you calculated in the first part (reworked for a 20mer) to an actual length. May be easier if you work it as 1 in x, then all you have to do divide the genome length l by x. Try my teaching site: mvls.gla.ac.uk/Teaching/SLS-GMC/ren.html. – David Mar 11 at 19:35