A school has to form a debate team of 3 students from 8 students. Two particular students cannot be on the same team. Which expression correctly gives the number of such teams?

Correct answer: \(\binom{8}{3}-\binom{6}{1}\)

There are \(\binom{8}{3}\) total teams. In every invalid team, both particular students are already chosen, so the third member is selected from the remaining 6 students: \(\binom{6}{1}\). Hence subtract \(\binom{6}{1}\). Exam tip: count forbidden cases separately before subtracting.