# Thread: how many bit strings of length 10 ...

1. ## how many bit strings of length 10 ...

how many bit strings of length 10 either start with 000 or end with 1111??????

Thank you very much

2. Hello,
Originally Posted by Narek
how many bit strings of length 10 either start with 000 or end with 1111??????

Thank you very much
Well, keep 000 at the beginning.
Then there are 7 remaining bits that are to be chosen.
Each with two possible values : 0 & 1.
So it's 2^7.

Now, keep 1111 in the end.
There are 6 remaining bits that are to be chosen.
Each with two possible values : 0 & 1.
So it's 2^6.

Total number : 2^7+2^6 (if you have to include the case where it both starts with 000 and ends with 1111)

3. ## Thank you

Thank you my friend,

you always explain so clearly and I really appreciate it.

4. Originally Posted by Moo

Total number : 2^7+2^6 (if you have to include the case where it both starts with 000 and ends with 1111)
But with that total, you've counted doubly those strings that begin with 000 and end with 1111. There are 2^3 such strings by the same reasoning, so you have to subtract those from the sum.

5. ## so the answer is ... ?

(2^7 + 2^6) - (2^3) = 184

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### how many bit string length 10 starting with 11 contain 0

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