2022 EJC J2 MYE P2 Q8

The Frisbee CCA has \(12\) students, comprising \(6\) male students and \(6\) female students.

1. Find the number of ways of grouping the students if
   1. there is one group of \(3\) students, one group of \(4\) students and one group of \(5\) students,[1]
   2. there are three groups of 4 students each, and there must be an equal number of male and female students in each group.[3]
2. How many ways can the students be arranged in a row if three particular female students must stand together, and the male students are not all standing together?[3]
3. The students are now seated in a circle. Find the number of ways to arrange the students if
   1. there are no restrictions,[1]
   2. the captain and vice-captain must not sit together.[2]