(a) A 5-character password is to be formed from the following 10 characters.

Letters: \(A,\ B,\ C,\ X,\ Y,\ Z\)

Symbols: *, $, #, &

No character can be used more than once in any 5-character password.

(i) Find the number of passwords that can be formed.

(ii) Find the number of passwords that can be formed if the password has to contain at least one symbol.

(iii) Find the number of passwords that can be formed if the password has to start with two letters and end with two symbols.

(b) A team of 8 people is to be chosen from 5 doctors, 4 teachers and 6 police officers. Find how many possible teams have the same number of doctors as teachers.