Practice Flashcards
Flip to reveal answersHow do you count arrangements where some people must stay together?
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All 8 Flashcards — Together restrictions
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Question
How do you count arrangements where some people must stay together?
Answer
Glue them into one block, arrange the blocks, then multiply by the ways to arrange inside the block.
Question
A block of k people has how many internal orders?
Answer
k! — the ways to arrange the k people inside the block.
Question
'A and B must sit together' — the method?
Answer
Treat AB as one block. Arrange the (n − 1) things, then × 2 for the AB / BA orders inside.
Question
'A immediately after B' vs 'A and B together' — what's different?
Answer
'Together' allows both internal orders (× 2). 'Immediately after' fixes the order (× 1).
Question
After gluing a block, how many things do you arrange?
Answer
One fewer for each extra person in the block — a block of k among n total leaves (n − k + 1) things to arrange.
Question
3 books must stay together among 7 — how many arrangements?
Answer
Glue the 3: arrange 5 things (5!) × 3! inside = 120 × 6 = 720.
Question
Why does 'immediately after' use × 1, not × 2?
Answer
The order inside the block is fixed (only one way), so there's nothing extra to multiply by.
Question
Trigger words for the block method?
Answer
'together', 'next to each other', 'side by side', 'consecutive', 'immediately after/before'.
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Topic 1.10 hub
Counting & binomial (HL only)
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