We flip a fair coin 10 times. What is the probability that we get heads in exactly 8 of the 10 flips?

We have a binomial probability

C(10, 8)  * (.5)^8 * (.5)^2  = 45 / 1024  ≈  4.4%

We can also represent these using combinations.

We have to find the value of \(\binom{10}{8}.\)

A quicker way is to recognize Pascal's triangle, and this is the tenth row, and the sum is \(2^{10}=1024.\) Thus, the answer is, \(\frac{\binom{10}{8}}{1024}=\boxed{\frac{45}{1024}}.\)