How many bit strings of length 10 have
a) exactly three 0s?
b) more 0s than 1s?
c) at least seven 1s?
d) at least three 1s?
How many bit strings of length 10 have exactly three 0s?
Answer: The bit strings have 10 positions: 1, 2, ..., 10. A bit string with exactly 3 0s can be described as a 3-subset of the numbers 1, 2, ..., 10. There are C(10, 3) such 3-subsets. So there are C(10,3)=120 bit strings of length 10 that have exactly three 0s.
How many bit strings of length 10 have more 0s than 1s?
Answer: There are 5 possibilities that have more 0s than 1s as follows:
i 6 0s and ...
The expert determines how many bit strings of length 10 have. Computations and permutations are determined.