Practice Flashcards
Flip to reveal answersA question says the digits must be in 'increasing order'. Arrange or choose?
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All 8 Flashcards — Forced order
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Question
A question says the digits must be in 'increasing order'. Arrange or choose?
Answer
Choose — the increasing order is fixed, so each set of digits gives exactly one number. Count with ⁿCᵣ.
Question
Why is 'increasing order' a selection, not an arrangement?
Answer
Once you pick the items, there is only ONE way to put them in increasing order — nothing is left to arrange, so order doesn't add anything.
Question
How many 4-digit numbers have strictly increasing digits?
Answer
Choose 4 from 1–9 (0 can't appear): ⁹C₄ = 126.
Question
Which wordings force the order (so you just choose)?
Answer
'increasing order', 'decreasing order', 'alphabetical order' — all fix the order, so use ⁿCᵣ.
Question
For increasing-digit numbers, why can't 0 be used?
Answer
In increasing order 0 would have to come first, but a number can't start with 0. So choose from 1–9.
Question
3 letters from A–G in alphabetical order — how many?
Answer
Choose 3 of the 7 letters: ⁷C₃ = 35 (alphabetical order is automatic).
Question
If you used ⁿPᵣ for an 'increasing order' question, what went wrong?
Answer
You counted the orderings, but the order is forced (one per set). Divide out — i.e. use ⁿCᵣ instead.
Question
Increasing order vs decreasing order — different counts?
Answer
No — both fix the order, so both are ⁿCᵣ. Each chosen set has one increasing and one decreasing arrangement.
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Full study notes for Forced order
Topic 1.10 hub
Counting & binomial (HL only)
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