You have to find 5 arrangements over 3 posibilities:

5!/2!*3! = 10

And now work with the probabilities:

10 * [(1/2)^3]*[(1/2)^2] =
10 * 1/8 * 1/4 =
10/32
5/16

billzhao wrote:If the probability of rain on any given day in city x is 50%, what is the probability if with rain on exactly 3 days in a five day period?

For this problem you need to use the binomial distribution formula or you can lay every possible outcome out:
R=Rain
N=No rain
so your possible outcomes are

RRRNN=.5^5
NRRRN=" "
NNRRR=" "
RNRNR=" "
RRNRN=" "
RRNNR=" "
... AND SO ON

The easy way out is the one mentioned above. Using combinations 5 choose 3. Total 10 possible arrangements. Pr(rain)^3 * Pr(no rain)^2
and as above you get the same 5/16.

Thanks All for your help!