?4: [52 marks] Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that

a) the bit string has exactly two 1s;

b) the bit string begins and ends with 0;

c) the bit string has the sum of its digits equal to seven;

d) the bit string has more 0s than 1s;

e) the bit string has exactly two 1s, given that the string begins with a 1.