Examples and practice
Permutations and combinations
Back to lessonPractice section 1 · Questions 1–6
Count the settings of a four-wheel lock · Add the air and sea travel alternatives · +4 more
Practice section 2 · Questions 7–12
Arrange STATISTICS without distinguishing repeated copies · Arrange MATHEMATICS by counting its repeated letters · +4 more
- Arrange STATISTICS without distinguishing repeated copies
- Arrange MATHEMATICS by counting its repeated letters
- Choose a committee or choose who is left out
- Select three of five people without assigning roles
- Count restricted committees using cases and complements
- Choose a committee subject to a married-couple restriction
Practice section 3 · Questions 13–18
Partition children into unlabelled groups · Divide ten people into repeated group sizes · +4 more
Practice section 4 · Questions 19–24
Arrange adjacent letters and form CELEBRATE codewords · Fill the most constrained digit position first · +4 more
Practice section 5 · Questions 25–30
Rearrange the ACE icon with repeated symbols · Seat ten people with two couples · +4 more
Practice section 6 · Questions 31–36
Separate disjoint cases from inclusion–exclusion · Keep a fixed-order block and separate two books · +4 more
- Separate disjoint cases from inclusion–exclusion
- Keep a fixed-order block and separate two books
- Count signals by their remaining colour multiplicities
- Distinguish circular rotations from numbered seats
- Separate repeated-ball selections into disjoint cases
- Classify code words by the number of repeated pairs
Practice section 7 · Questions 37–42
Count nonempty subsets and a selection with tomatoes fixed · Keep all ten seats when people are absent · +4 more
- Count nonempty subsets and a selection with tomatoes fixed
- Keep all ten seats when people are absent
- Join overlapping card blocks before arranging the remaining cards
- Choose people while controlling complete couples
- Separate fixed digit counts from adjacent-repeat complements
- Allow leading zero in a six-position PIN
Practice section 8 · Questions 43–48
Choose three gaps for the three vowels · Distinguish nine-digit integers from nine-position binary strings · +4 more
Practice section 9 · Questions 49–54
Use flavour multiplicities rather than physical bar identities · Keep the meeting and lunch seating models separate · +4 more
- Use flavour multiplicities rather than physical bar identities
- Keep the meeting and lunch seating models separate
- Separate labelled circular seats from fixed-room colour assignments
- Keep committee choices, circular seating and diner choices distinct
- Explain every complement and the meaning of neighbouring ride seats
- Split a parent–child–parent block by its table
Practice section 10 · Question 55
Reserve the central front-row positions before placing the children