Hint
Objects are distinct and selections are without replacement. Fill r ordered positions without replacement.
Worked solution
(a)
Fill r ordered positions without replacement.
\(90\)
Answer: \(90\)
(b)
Divide ordered choices by r!.
\(45\)
Answer: \(45\)
(c)
Treat the two labels as one block, with two internal orders.
\(725760\)
Answer: \(725760\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternatives and consequential reasoning; an unexplained final answer does not earn a method mark.
(a) · 2 marks
- 1 mark: Fill r ordered positions without replacement.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Do not use permutations for an unlabelled committee.
(b) · 2 marks
- 1 mark: Divide ordered choices by r!.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: An adjacent pair can have two internal orders.
(c) · 2 marks
- 1 mark: Treat the two labels as one block, with two internal orders.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Do not use permutations for an unlabelled committee.
Total: 6 marks.