1.10: 6-digit numbers and party invitations

0606/13/O/N/17 — Question 9 · 9 marks

(a)(i)
A 6-digit number is to be formed using the digits 1, 3, 5, 6, 8, 9. Each of these digits may be used only once in any 6-digit number. Find how many different 6-digit numbers can be formed if there are no restrictions.
[1]
(a)(ii)
A 6-digit number is to be formed using the digits 1, 3, 5, 6, 8, 9. Each of these digits may be used only once in any 6-digit number. Find how many different 6-digit numbers can be formed if the number formed is even.
[1]
(a)(iii)
A 6-digit number is to be formed using the digits 1, 3, 5, 6, 8, 9. Each of these digits may be used only once in any 6-digit number. Find how many different 6-digit numbers can be formed if the number formed is even and greater than 300000.
[3]
(b)(i)
Ruby wants to have a party for her friends. She can only invite 8 of her 15 friends. Find the number of different ways she can choose her friends for the party if there are no restrictions.
[1]
(b)(ii)
Ruby wants to have a party for her friends. She can only invite 8 of her 15 friends. Two of her 15 friends are twins who cannot be separated. Find the number of different ways she can now choose her friends for the party.
[3]