2021 HSC Mathematics Extension 1
Question 11(d):
Combinatorics
A committee containing men and women is to be formed from a group of men and women.
In how many different ways can the committee be formed?
How to recognise this question
Question type: combinatorics
- The command and notation point to combinatorics.
- The requested response is a short answer.
How to handle it: count a simple unrestricted set first, then add or subtract the arrangements that break the condition.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Choose men from : . Choose women from : .
- Independent choices multiply: .
- NESA: 1 mark for (or unsimplified if accepted as complete).
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
A committee of men and women is formed from men and women. How many ways?
Question 2
From men and women, form a committee of men and women. How many ways?
Question 3
From men and women, form a committee of men and women. How many ways?