CAIE A-Level Mathematics A2 5.2.2 Arrangement Restrictions Questions
Practise counting arrangements of repeated objects and applying positional and grouping restrictions.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- count arrangements when objects or letters are repeated
- apply adjacency, grouping and positional restrictions
- combine permutation methods to solve constrained arrangement problems
CAIE A-Level Mathematics A2 5.2.2 Arrangement Restrictions Questions question 1
[Maximum number: 4]
Question (a)
(a)
How many different arrangements are there of the 9 letters in the word RECORDERS?
The repeated letters are the three R's and the two E's. Hence the number of arrangements is
2!3!9!=30240.
Question (b)
(b)
How many different arrangements are there of the 9 letters in the word RECORDERS in which there is an E at the beginning, an E at the end and the three Rs are not all together?
With an E at each end, the number of arrangements is 7!/3!. If the three R's are together, the number is 5!. Therefore,
3!7!−5!=840−120=720.
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