2023 HSC Mathematics Extension 1
Question 11(b):
Combinatorics
In how many different ways can all the letters of the word CONDOBOLIN be arranged in a line?
How to recognise this question
Question type: combinatorics
- The command and notation point to combinatorics.
- The requested response is a worked solution.
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
- CONDOBOLIN has letters: C, O, N, D, O, B, O, L, I, N.
- Letter multiplicities: O appears times, N appears times; other letters once.
- Number of distinct linear arrangements: .
- NESA: 2 marks for correct solution; 1 mark for dividing by a relevant number, or equivalent merit.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks 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
How many distinct linear arrangements of the letters in MISSISSIPPI are there?
Question 2
Find the number of distinct arrangements of the letters in BANANA.
Question 3
How many linear arrangements of VECTOR are there?