# Permutations and Combinations of Strengths

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12. How many bit strings of length 12 contain

a) exactly three 1s?

b) at most three 1 s?

c) at least three 1 s?

d) an equal number of 0s and 1s?

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Permutations and combinations are infused in this solution.

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12. How many bit strings of length 12 contain

a) exactly three 1s?

b) at most three 1 s?

c) at least three 1 s?

d) an equal number of 0s and 1s?

We assume that no string starts with a zero.

a) For exactly three 1s to be there in the string of length 12, there should be nine 0s and three 1s with the left most place filled with a 1.

So, the remaining 11 places can be filled with two 1s and ...

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