Selections (order doesn't matter)
Practice Flashcards
Flip to reveal answersWhen should you use a selection, ⁿCᵣ?
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Question
When should you use a selection, ⁿCᵣ?
Answer
When you pick a GROUP and the order inside doesn't matter — a team, a committee, a sample. {A,B} is the same as {B,A}.
Question
State the quick rule for ⁿCᵣ.
Answer
Top: r numbers counting down from n. Bottom: r! = r × (r − 1) × … × 1. e.g. ⁵C₂ = (5 × 4)/(2 × 1) = 10.
Question
Why does ⁿCᵣ divide by r!?
Answer
Picking r in order counts each group r! times (its r! orderings). A group has no order, so divide those out.
Question
Selection or arrangement — how do you tell?
Answer
Ask: does the order matter? Order matters → arrangement (ⁿPᵣ). Order doesn't → selection (ⁿCᵣ).
Question
State the full formula for ⁿCᵣ.
Answer
ⁿCᵣ = n!/(r!(n − r)!) — the number of ways to choose r objects from n with order ignored.
Question
Compute ⁸C₃ by hand.
Answer
(8 × 7 × 6)/(3 × 2 × 1) = 336/6 = 56.
Question
On Paper 2, where is nCr on the TI-84?
Answer
MATH, arrow right to PRB, then 3: nCr. Type n, choose nCr, type r, ENTER.
Question
Team, committee, sample, handful — which formula?
Answer
ⁿCᵣ — these are unordered groups, so order doesn't matter.
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Topic 1.10 hub
Counting & binomial (HL only)
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