1.11: 5-digit codes and team selection

0606/13/O/N/19 — Question 7 · 9 marks

(a)(i)
A 5-digit code is to be chosen from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit may be used once only in any 5-digit code. Find the number of different 5-digit codes that may be chosen if there are no restrictions.
[1]
(a)(ii)
A 5-digit code is to be chosen from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit may be used once only in any 5-digit code. Find the number of different 5-digit codes that may be chosen if the code is divisible by 5.
[1]
(a)(iii)
A 5-digit code is to be chosen from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. Each digit may be used once only in any 5-digit code. Find the number of different 5-digit codes that may be chosen if the code is even and greater than 70000.
[3]
(b)(i)
A team of 6 people is to be chosen from 8 men and 6 women. Find the number of different teams that may be chosen if there are no restrictions.
[1]
(b)(ii)
A team of 6 people is to be chosen from 8 men and 6 women. Find the number of different teams that may be chosen if there are no women in the team.
[1]
(b)(iii)
A team of 6 people is to be chosen from 8 men and 6 women. There are a husband and wife who must not be separated. Find the number of different teams that may be chosen.
[3]