Alternatively, albeit not as fast, one could look at the total number of teams that can be formed without constraint, which is \(8C_5 = 56\) and subtract the teams that contain three teachers, which is \(5C_2 = 10\) as well as the number of teams that contain no teachers, which is just \(1\).
\(56 - 10 - 1 = 45\) -> (D)
\(56 - 10 - 1 = 45\) -> (D)
