2.2: Captain selection and teacher teams

0606/21/M/J/17 — Question 8 · 7 marks

(a)
A football club has 30 players. In how many different ways can a captain and a vice-captain be selected at random from these players?
[1]
(b)(i)
A team of 11 teachers is to be chosen from 2 mathematics teachers, 5 computing teachers and 9 science teachers. Find the number of different teams that can be chosen if the team must have exactly 1 mathematics teacher.
[2]
(b)(ii)
A team of 11 teachers is to be chosen from 2 mathematics teachers, 5 computing teachers and 9 science teachers. Find the number of different teams that can be chosen if the team must have exactly 1 mathematics teacher and at least 4 computing teachers.
[4]