The committee could be made in 6,720 ways
Explanation:Parameters:
• Total number of teachers avalable = 8
• Number of teachers to be chosen from this = 5
• Total number of students = 10
• Number of students to be chosen from this = 3
We have number of ways for each group to be:
Teachers:
[tex]\begin{gathered} 8C5=\frac{8!}{(8-5)!5!} \\ \\ =\frac{8!}{3!5!}=\frac{8\times7\times6}{3\times2\times1}=56 \end{gathered}[/tex]Students:
[tex]\begin{gathered} 10C3=\frac{10!}{(10-3)!3!} \\ \\ =\frac{10!}{7!3!}=\frac{10\times9\times8}{3\times2\times1}=120 \end{gathered}[/tex]Finally, the committee could be made in
[tex]120\times56=6,720ways[/tex]