How many bit strings of length 60 are there such that:

a.) The bit string has at most twenty-five 0s and at most thirty-seven 1s. Additionally, the bit string corresponding to the first thirty-one positions contains at least seven 0s and at least twenty-four 1s, and the bit string corresponding to the last seventeen positions contains at least fifteen 0s.

b.) The bit string corresponding to the first eight positions has exactly three 1s and the bit string corresponding to the last thirty-five positions contains the string 01111011 as a substring.

I think I was able to partially find a solution for a. but honestly I would like to understand how to solve these kind of exercises.