Arrangements (order matters)
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Flip to reveal answersWhat makes a counting question an 'arrangement'?
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All 10 Flashcards — Arrangements (order matters)
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Question
What makes a counting question an 'arrangement'?
Answer
Order matters — the position of each object counts, so ABC and CBA are different. Count by filling positions and multiplying.
Question
Describe the box method for arrangements.
Answer
Draw one box per position, write how many choices go in each box, then multiply. Fill the most restricted box first.
Question
How do you count r-digit numbers with no leading zero?
Answer
The first box has 9 choices (1–9, not 0); fill the rest from the remaining digits, then multiply.
Question
How do you arrange ALL n distinct objects in a row?
Answer
n! = n × (n − 1) × … × 1. Example: 9 people in a line = 9! = 362880.
Question
State the formula for ⁿPᵣ and what it counts.
Answer
ⁿPᵣ = n!/(n − r)! — the number of ways to arrange r objects out of n in a definite order.
Question
How is ⁿPᵣ just the multiplication idea?
Answer
It multiplies r numbers counting down from n: n × (n − 1) × … (r factors). e.g. ⁸P₃ = 8 × 7 × 6 = 336.
Question
Arrange ALL of them vs SOME of them — which formula?
Answer
All n → n!. Just r of them, in order → ⁿPᵣ = n!/(n − r)!.
Question
Seats, finishing orders, codes — arrangement or not?
Answer
Arrangements — the position matters, so use n! (all) or ⁿPᵣ (some), filling positions and multiplying.
Question
On Paper 2, where is nPr on the TI-84?
Answer
MATH, arrow right to PRB, then 2: nPr. Type n, choose nPr, type r, ENTER.
Question
What is ⁿPₙ equal to?
Answer
n! — arranging all n in order (since n!/(n − n)! = n!/0! = n!).
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Topic 1.10 hub
Counting & binomial (HL only)
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