Here is how the question is posed:
Let $s_1$, $s_2$, $s_3, \ldots, s_{90}$ be 90 bit strings of length nine or less. Prove that there exist two strings $s_i$ and $s_j$ with $i \neq j$ that contain the same number of 0s and the same number of 1s (for example, 10110 and 11100).
I've tried figuring out how many bit strings of length nine have one 1 and eight zeroes, two 1s and 7 zeroes, etc. But I'm still confused...
Any idea how I might approach this? Thanks!