# Thread: [SOLVED] Help with some bit string counting questions

1. ## [SOLVED] Help with some bit string counting questions

I don't have any issues with calculation on these problems, but I worry that the semantics of these problems may change how they are meant to be calculated. I've provided the questions and my current answers.

How many bit strings of length 16 contain

a) Exactly 4 more ones than zeros?
Current answer: $\frac{16!}{10!6!}=8008$

b) Exactly 2 ones and 14 zeros?
Current answer: $\frac{16!}{14!2!}=120$

c) Three times as many ones as zeros?
Current answer: $\frac{16!}{4!12!}=1820$

I can't shake the feeling that the way these questions are worded changes their meaning. Can someone confirm my answers?

2. Originally Posted by Runty
How many bit strings of length 16 contain
a) Exactly 4 more ones than zeros?
Current answer: $\frac{16!}{10!6!}=8008$

b) Exactly 2 ones and 14 zeros?
Current answer: $\frac{16!}{14!2!}=120$

c) Three times as many ones as zeros?
Current answer: $\frac{16!}{4!12!}=1820$
They are correct.

3. Originally Posted by Plato
They are correct.
Thanks for helping me make sure of that. I wasn't entirely sure of the semantics, so I needed to confirm it.