jmc

There are $2^{10}=1024$ possible outcomes of the 10 coin flips. There are $\left(\genfrac{}{}{0ex}{}{10}{8}\right)=\left(\genfrac{}{}{0ex}{}{10}{2}\right)=45$ ways to get exactly 8 heads, so the probability is $\frac{45}{2^{10}}=\boxed{\frac{45}{1024}}$.