[Math] How many bit strings of length 17 contain at least 5 ones

combinatoricsdiscrete mathematicspermutations

I'm a really confused as to how to start this question, would really appreciate any help you guys could give me!

Best Answer

How many total bit strings of that length are there? There are $\binom{17}{k}$ bit strings of length $17$ with exactly $k$ ones, since choosing the positions of all the ones determines the string completely. It will be quicker to find the number of bit strings that don't meet your criterion, then subtract them from the total.

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