2023 EJC P2 Q9

A personality test assesses \(32\) key traits. These \(32\) traits are grouped into \(4\) domains – Cognition, Influence, Rapport and Planning – with each domain consisting of \(8\) traits. The test result for a person consists of his/her top \(5\) traits in ascending order of strength.

1. Find the number of different results that the personality test can produce.[2]
2. Find the number of different results that can be produced with traits from at least \(2\) domains.[2]
3. Find the number of different results that can be produced with at least one trait from each domain and neither of the top \(2\) traits are from the Cognition domain.[3]
4. A result contains \(2\) particular traits from Rapport, \(2\) particular traits from Planning and \(1\) particular trait from Influence. Find the number of different possible results that can be produced with no consecutive traits from the same domain.[3]