# 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?

https://brainmass.com/math/combinatorics/computations-permutations-514200

#### 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.

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