Answer:
The number of ways is 13860 ways
Step-by-step explanation:
Given
Senior Members = 10
Junior Members = 12
Required
Number of ways of selecting 6 students students
The question lay emphasis on the keyword selection; this implies combination
From the question, we understand that
4 students are to be selected from senior members while 2 from junior members;
The number of ways is calculated as thus;
Ways = Ways of Selecting Senior Members * Ways of Selecting Junior Members
[tex]Ways = ^{10}C_4 * ^{12}C2[/tex]
[tex]Ways = \frac{10!}{(10-4)!4!)} * \frac{12!}{(12-2)!2!)}[/tex]
[tex]Ways = \frac{10!}{(6)!4!)} * \frac{12!}{(10)!2!)}[/tex]
[tex]Ways = \frac{10 * 9 * 8 * 7 *6!}{(6! * 4*3*2*1)} * \frac{12*11*10!}{(10!*2*1)}[/tex]
[tex]Ways = \frac{10 * 9 * 8 * 7}{4*3*2*1} * \frac{12*11}{2*1}[/tex]
[tex]Ways = \frac{5040}{24} * \frac{132}{2}[/tex]
[tex]Ways = 210 * 66[/tex]
[tex]Ways = 13860[/tex]
Hence, the number of ways is 13860 ways
