There's a little surprise in there. I won't spoil the fun. (Until I do.
Update (also in comments): The weird thing, that you might notice in the course of solving, if you calculate P(5), P(6), and P(7) separately and then add them together, is that P(5) and P(6) come out to the same thing. The probability it will rain 5 out of the 7 days is the SAME as the probability it will rain 6 out of the 7 days. Isn't that weird? If you write it out with fractions and the nCr formula you can how it happens, but the result is still counterintuitive to me. Combinations sometimes surprise me like that.