Both problems are applications of the Binomial Distribution...

Pr{X} = N!/(X!*(N-X)!) * p^X * q^(N-X) where p is the probability of success and q = 1 - p.

For example, your second question is solved by using for formula above as:

Pr{X=8} = 11!/(8!*3!) * (.5)^8 * (.5)^3 where p=0.5 because voting is random.