Answer:
8190 ways
Step-by-step explanation:
Given
[tex]Teachers = 6[/tex]
[tex]Students = 15[/tex]
Selection
[tex]Students = 4[/tex]
[tex]Teachers = 5[/tex]
Required
Number of ways of selection
4 students can be selected from 15 students in:
[tex]Students= ^{15}C_4[/tex]
Similarly.
5 teachers can be selected from 6 teachers in:
[tex]Teachers= ^{6}C_5[/tex]
So, the required number of selection is:
[tex]Selection = ^{15}C_4 * ^6C_5[/tex]
Apply combination formula:
[tex]Selection = \frac{15!}{(15-4)!4!} * \frac{6!}{(6-5)!5!}[/tex]
[tex]Selection = \frac{15!}{11!4!} * \frac{6!}{1!5!}[/tex]
[tex]Selection = \frac{15*14*13*12*11!}{11!*4*3*2*1} * \frac{6*5!}{1*5!}[/tex]
[tex]Selection = \frac{15*14*13*12}{4*3*2*1} * \frac{6}{1}[/tex]
[tex]Selection = \frac{32760}{24} * 6[/tex]
[tex]Selection = 1365 * 6[/tex]
[tex]Selection = 8190[/tex]
