3.45: Team selection and a product of permutations

0606/11/M/J/23 — Question 7 · 7 marks

(a)(i)
Find the number of different teams of 8 that can be chosen from 15 people.
[1]
(a)(ii)
Find the number of teams if a family of 4 must be kept together.
[3]
(b)
Given that nP9nP10=243n+1\dfrac{{}^{n}P_{9}}{{}^{n}P_{10}} = \dfrac{243}{n + 1}, find the value of nn.
[3]