Question

- Angela, Barry and Carmelina are in a drama qub with 12 other students (15 total students). A group of 4 peoplewill be selected to design the stage for the next production. How many ways can the group of 4 be chosen...a) ... so that Angela is selected for the group, but Barry and Carmelina are not selected for the group.b) ..so that Angela, Barry and Carmelina are all selected for the group OR are all not selected for the group.(They can't be split up!)

Answer 1

Given:

The number of students in the class is n = 12.

The number of groups formed is k = 4

The number of students in each group is h = 3.

Explanation:

The formula for the number of ways to divide n students in k groups with each group has h students is,

$\frac{n!}{(h!)^kk!}$

Substitute the values in the formula to determine the number of ways.

$\begin{gathered} \frac{12!}{(3!)^4(4!)}=\frac{12!}{(3!)(3!)(3!)(3!)(4!)} \\ =15400 \end{gathered}$

So teacher can divide 12 students in 4 different groups such that each group has 3 students is 15400 ways.