2024 RI H1 Q7

A Mathematics club with \(n\) members plans to form a recruitment committee consisting of five members. It is known that there are \(42504\) ways to form this committee.

1. Find the value of \(n\).[1]

A few members did not want to be in the committee, so at the end the committee is formed from \(18\) members. Two of the \(18\) members are Ana and Elsa. In how many ways can the committee be formed if

2. both Ana and Elsa are included,[1]
3. it must include either Ana or Elsa but not both.[2]

The final committee that was formed included both Ana and Elsa, and they needed to take a photo, sitting in a row, for the school magazine.

4. In how many ways can the five committee members sit in a row if Ana and Elsa must be seated together, with Ana always seated on the left of Elsa?[2]