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A committee must be formed with 5 teachers and 4 students. If there are 6 teachers to choose from, and 15 students, how many different ways could the committee be mad?

1 Answer

10 votes

Answer:

8190 ways

Explanation:

Given


Teachers = 6


Students = 15

Selection


Students = 4


Teachers = 5

Required

Number of ways of selection

4 students can be selected from 15 students in:


Students= ^(15)C_4

Similarly.

5 teachers can be selected from 6 teachers in:


Teachers= ^(6)C_5

So, the required number of selection is:


Selection = ^(15)C_4 * ^6C_5

Apply combination formula:


Selection = (15!)/((15-4)!4!) * (6!)/((6-5)!5!)


Selection = (15!)/(11!4!) * (6!)/(1!5!)


Selection = (15*14*13*12*11!)/(11!*4*3*2*1) * (6*5!)/(1*5!)


Selection = (15*14*13*12)/(4*3*2*1) * (6)/(1)


Selection = (32760)/(24) * 6


Selection = 1365 * 6


Selection = 8190

User Milad Zahedi
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