3.10: Committee selection and a permutations equation

0606/13/M/J/21 — Question 7 · 8 marks

A committee of 8 people is to be formed from 5 teachers, 4 doctors and 3 police officers.

(a)(i)

Find the number of different committees that could be chosen if all 4 doctors are on the committee.

[2]

(a)(ii)

Find the number of different committees that could be chosen if there are at least 2 teachers on the committee.

[3]

(b)

Given that

{}^{n}P_{5} = 6\,{}^{n-1}P_{4}

, find the value of

n

[3]