Question

In how many ways can a subcommittee of 6 students be chosen from a committee which consists of 10 senior members and 12 junior members if the team must consist of 4 senior members and 2 junior members?

Answer 1

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

$Ways = ^{10}C_4 * ^{12}C2$

$Ways = \frac{10!}{(10-4)!4!)} * \frac{12!}{(12-2)!2!)}$

$Ways = \frac{10!}{(6)!4!)} * \frac{12!}{(10)!2!)}$

$Ways = \frac{10 * 9 * 8 * 7 *6!}{(6! * 4*3*2*1)} * \frac{12*11*10!}{(10!*2*1)}$

$Ways = \frac{10 * 9 * 8 * 7}{4*3*2*1} * \frac{12*11}{2*1}$

$Ways = \frac{5040}{24} * \frac{132}{2}$

$Ways = 210 * 66$

$Ways = 13860$

Hence, the number of ways is 13860 ways