The Question
What is the probability that a binary string of length 16, chosen uniformly from all binary strings of length 16, has exactly eight 1s.
My Work
There are $2^{16}$ binary strings of length 16. Therefore, our sample space is $2^{16}$.
We can make a binary string of length 16 like so: Select 8 spaces to place our $1$s $\binom{16}{8}$ ways to do this, and then fill the remaining spaces with $0$s.
Therefore, the probability of our event = $\frac{\binom{16}{8}}{2^{16}}$
My Question
I don't have a solution for this question available (Checked book and internet). Wondering if what I did was correct