Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- anonymous

How many bit strings of length 12 contain
a) exactly three 1s?
b) at most three 1s?
c) at least three 1s?
d) an equal number of 0s and 1s?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

Get your **free** account and access **expert** answers to this and **thousands** of other questions

- anonymous

- katieb

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- KingGeorge

a. 12-choose-3 Since you're choosing three places for a one to go.

- KingGeorge

b. \[\binom{12}{0} + \binom{12}{1} + \binom{12}{2} +\binom{12}{3}\]

- KingGeorge

c. \[2^{12}-\left[\binom{12}{0} + \binom{12}{1} + \binom{12}{2}\right]\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- KingGeorge

d.\[\binom{12}{6}\]

- KingGeorge

If you want an explanation for any one of these, please ask.

- inkyvoyd

Wrong, all of those. I'm pretty sure that that format means combination, while you're looking for permutations.

- anonymous

i think that the problem seeks combinations actually, i just don't know how to come up with these numbers.

- anonymous

or wait.. okay im confused. haha. permutations because order matters in bit strings?

- inkyvoyd

No, Permutations because order matters. 111000000000 is different from 011100000000 is it not?

- anonymous

haha okay thanks for clearing that up.

- inkyvoyd

If you ever get confused about whether to use permutations or combinations, just remember the order matters rule for permutations.

- KingGeorge

Sorry, had to step away for a little. You definitely want combinations here.
Suppose you have this string: 111000000000. If you were using permutations, you would have \(3! \cdot 9!\) ways to make this string. However, there is only one string that looks like this, not \(3!\cdot9!\) strings.
In this problem, order does not matter because we're considering the order of the ones with relation to the other ones. Since \(1=1\), order does not matter.

- anonymous

I see.. wow thanks!

Looking for something else?

Not the answer you are looking for? Search for more explanations.