Suppose that you want to pick a binary string (a string consisting of only 1's and 0's) from the set of all binary strings of length 8.

1. What is the probability that the binary string has exactly five 1's?
2. What is the probability that the binary string has exactly two 1's, given that the string begins with a 1?
3. What is the probability that the binary string has more 0's than 1's?
4. What is the probability that the binary string has the sum of its digits equal to five?

Leave your answer in combination form. You do not need to simplify/calculate out value.