Let's say 4 players, A, B, C , and D are playing bridge. (Each player is dealt 13 cards and random from standard 52 card deck).
What is the number of ways that all cards of two suits are split among players A and B?
I got ${4\choose2}{26\choose13}{13\choose13}{26\choose13}{13\choose13}$. We first select which 2 suits go to players A and B then we select 13 cards out of the 26 for A, then there only remain 13 cards B can select so B takes the remaining. Of all 26 cards remaining, we give 13 to C and the rest to D
Your answer is correct. There are $\binom{4}2\binom{26}{13}^2$ ways that $A$ and $B$ receive all of the cards of two suits, where the order of cards within a hand does not matter.