2019 Cayley Problem 22

Seven friends are riding the bus to school:

- Cha and Bai are on 2 different buses. - Bai, Abu and Don are on 3 different buses. - Don, Gia and Fan are on 3 different buses. - Abu, Eva and Bai are on 3 different buses. - Gia and Eva are on 2 different buses. - Fan, Cha and Gia are on 3 different buses. - Cha and Eva are on 2 different buses.

What is the least possible number of buses on which the friends could be riding?

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 5\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 7

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.