Math Help - Choose question

1. Choose question

I am working on some problems using binomial coefficients and am wondering if I am doing things correctly.

One question...

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

(10C3)(2)^7+(10C4)(2)^6

I don't think that is correct because the order matters in this case right? Though I am not sure how to take that into account.

2. Re: Choose question

Originally Posted by ehpoc
How many bit strings of length 10 either start with 000 or end with 1111?
(10C3)(2)^7+(10C4)(2)^6
Let $A$ be the set of 10-bit strings $000\cdots$.
Let $B$ be the set of 10-bit strings $\cdots 1111$.

Now you want $\|A\cup B\|=\|A\|+\| B\|-\|A\cap B\|.$