(a) A team of 8 people is to be chosen from a group of 15 people.

(i) Find the number of possible teams.

(ii) Four members of the group are from the same family. The team must include either all four family members or none of them. Find the number of possible teams.

(b) Given that

\(\displaystyle (n+9)\times{}^nP_{10}=(n^2+243)\times{}^{n-1}P_9,\)

find the value of \(n\).