Separation restrictions
Practice Flashcards
Flip to reveal answersHow do you count arrangements where two people must NOT be together?
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All 8 Flashcards — Separation restrictions
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Question
How do you count arrangements where two people must NOT be together?
Answer
Total − together. Count all arrangements, then subtract the ones where the two ARE together (block method).
Question
How do you count 'no two of a group adjacent'?
Answer
Gap method: arrange the other items first; they make gaps; place the restricted items into different gaps.
Question
How many gaps do n seated items make?
Answer
n + 1 gaps — one between each pair plus one at each end.
Question
In the gap method, why use ⁿPᵣ for placing the restricted items?
Answer
They go into different gaps and the items are distinct, so the order in which gaps are filled matters → ⁿPᵣ.
Question
'5 friends, A and B not together' — how many?
Answer
5! − (4! × 2) = 120 − 48 = 72.
Question
'4 boys, 2 girls, no two girls adjacent' — how many?
Answer
Boys 4! = 24, 5 gaps, girls ⁵P₂ = 20: 24 × 20 = 480.
Question
'Not together' vs 'no two adjacent' — which method?
Answer
A single pair not together → total − together. A whole group with none adjacent → the gap method.
Question
Trigger words for separation questions?
Answer
'not next to', 'not adjacent', 'apart', 'at least one seat between', 'not sharing a boundary'.
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Topic 1.10 hub
Counting & binomial (HL only)
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Math AA exam skills
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