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    Computations and permutations

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    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?

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    Solution Preview

    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 ...

    Solution Summary

    The expert determines how many bit strings of length 10 have. Computations and permutations are determined.