What is the minimum number of bits required to store each binary string of length 50? (b) what is the minimum number of bits required to store each number with 9 base ten digits? (c) what is the minimum number of bits required to store each length 10 fixed-density binary string with 4 ones?

In order to answer the above question, you should know the general rule to solve these questions.
The general rule states that there are 2ⁿ subsets of a set with n number of elements and we can use the logarithmic function to get the required number of bits.
That is: 
log₂(2ⁿ) = n number of bits

a). What is the minimum number of bits required to store each binary string of length 50?

In this situation, we have n = 50. Therefore,  2⁵⁰ binary strings of length 50 are there and so it would require:

                                                     log₂(2⁵⁰) = 50 bits.

b). what is the minimum number of bits required to store each number with 9 base of ten digits?

In this situation, we have n = 50. Therefore, 10⁹ numbers with 9 base ten digits are there and so it would require:

                                                     log2(109)= 29.89 
                                                                     = 30 bits. (rounded to the nearest                                                                                                                        whole #)

c).  what is the minimum number of bits required to store each length 10 fixed-density binary string with 4 ones?

There is (10,4) length 10 fixed density binary strings with 4 ones and
so it would require:
                                                     log₂(10,4)=log₂(210) = 7.7
                                                                    = 8 bits. (rounded to the nearest                                                                                                                        whole #)