1.4: 5-digit numbers and birthday party invitations

0606/12/M/J/17 — Question 8 · 11 marks

(a)(i)
A 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. Each digit can only be used once in any 5-digit number. Find the number of different 5-digit numbers that can be formed if there are no restrictions.
[1]
(a)(ii)
A 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. Each digit can only be used once in any 5-digit number. Find the number of different 5-digit numbers that can be formed if the number is divisible by 5.
[1]
(a)(iii)
A 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. Each digit can only be used once in any 5-digit number. Find the number of different 5-digit numbers that can be formed if the number is greater than 60000.
[1]
(a)(iv)
A 5-digit number is to be formed from the seven digits 1, 2, 3, 5, 6, 8 and 9. Each digit can only be used once in any 5-digit number. Find the number of different 5-digit numbers that can be formed if the number is greater than 60000 and even.
[3]
(b)(i)
Ranjit has 25 friends of whom 15 are boys and 10 are girls. Ranjit wishes to hold a birthday party but can only invite 7 friends. Find the number of different ways these 7 friends can be selected if there are no restrictions.
[1]
(b)(ii)
Ranjit has 25 friends of whom 15 are boys and 10 are girls. Ranjit wishes to hold a birthday party but can only invite 7 friends. Find the number of different ways these 7 friends can be selected if only 2 of the 7 friends are boys.
[1]
(b)(iii)
Ranjit has 25 friends of whom 15 are boys and 10 are girls. Ranjit wishes to hold a birthday party but can only invite 7 friends. The 25 friends include a boy and his sister who cannot be separated. Find the number of different ways these 7 friends can be selected.
[3]