Mathematics: 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?

A committee must be formed with 5 teachers and - id5410420214, emilylittle2442

1234Shutthedoor

17.03.2022

8190 ways

Step-by-step 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:

$Selection = \frac{15!}{(15-4)!4!} * \frac{6!}{(6-5)!5!}$

$Selection = \frac{15!}{11!4!} * \frac{6!}{1!5!}$

$Selection = \frac{15*14*13*12*11!}{11!*4*3*2*1} * \frac{6*5!}{1*5!}$

$Selection = \frac{15*14*13*12}{4*3*2*1} * \frac{6}{1}$

$Selection = \frac{32760}{24} * 6$

Selection = 1365 * 6

Selection = 8190

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MegRasmussen31

11.12.2022

3.5

Step-by-step explanation:

Whenever you do 2.25 x 4 you get 9, then you add 7.50 and get 16.5. Afterwards, you subtract 3.5 from 20 leaving you with $3.5 dollars.

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