Hint
The objects are distinct unless repetition is explicitly specified. Divide the ordered count by 3!.
Worked solution
(a)
\(\binom{5}{3}=10\)
Answer: \(10\).
Answer: \(10\)
(b)
\(\displaystyle \frac{5!}{(5- 3)!}= 60\)
Answer: \(60\).
Answer: \(60\)
(c)
\(2(5-1)!=48\)
Answer: \(48\).
Answer: \(48\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Divide the ordered count by 3!.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not use n! when only r positions are filled.
(b) · 2 marks
- 1 mark: Fill three labelled positions without replacement.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: A fixed pair in a block still has two possible internal orders.
(c) · 2 marks
- 1 mark: Treat A and B as one block with two internal orders.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not use n! when only r positions are filled.
Total: 6 marks.