Permutations, Combination and Binomial Expansion — Flashcards
Gujarat Board · Class 11 · Statistics
22 flashcards for Permutations, Combination and Binomial Expansion (Gujarat Board Class 11 Statistics) to test yourself on key terms and facts.
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What is the Fundamental Principle of Counting for Addition?
Answer
If there are m distinct things in Group 1 and n distinct things in Group 2, then selection of one thing from the combined groups can be done in m + n ways. The keyword 'OR' indicates addition. Example…
What is the Fundamental Principle of Counting for Multiplication?
Answer
If the first operation can be done in m ways and the second operation can be done in n ways, then both operations together can be done in m × n ways. The keyword 'AND' indicates multiplication. Exampl…
What is n! (n factorial) and how is it calculated?
Answer
n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1 It is the product of all natural numbers from 1 to n. Examples: 5! = 5 × 4 × 3 × 2 × 1 = 120 3! = 3 × 2 × 1 = 6 1! = 1 0! = 1 (by definition)…
Define Permutation and state its formula.
Answer
Permutation is the arrangement of r distinct things out of n distinct things where ORDER MATTERS. Formula: ⁿPᵣ = n!/(n-r)! where n ≥ r ≥ 0 Example: Arranging 3 students out of 5 students in 3 chairs =…
What are the important special cases of Permutation?
Answer
ⁿP₀ = 1 (no arrangements) ⁿPₙ = n! (all things arranged) ⁿP₁ = n (one thing from n) ⁿPₙ₋₁ = n! (leave one thing out) Examples: ⁵P₀ = 1, ⁵P₅ = 5! = 120, ⁵P₁ = 5, ⁵P₄ = 5! = 120…
Define Combination and state its formula.
Answer
Combination is the selection of r things out of n distinct things where ORDER DOES NOT MATTER. Formula: ⁿCᵣ = n!/[r!(n-r)!] where n ≥ r ≥ 0 Example: Selecting 3 friends out of 5 friends = ⁵C₃ = 5!/(3!
What is the relationship between Permutation and Combination?
Answer
ⁿPᵣ = ⁿCᵣ × r! OR ⁿCᵣ = ⁿPᵣ/r! This means: For each combination of r things, there are r! different arrangements (permutations). Example: ⁵C₃ = 10 combinations, but ⁵P₃ = 10 × 3! = 60 permutations…
What are the important special cases of Combination?
Answer
ⁿC₀ = 1 (select nothing) ⁿCₙ = 1 (select everything) ⁿC₁ = n (select one thing) ⁿCₙ₋₁ = n (leave one thing) ⁿCᵣ = ⁿCₙ₋ᵣ (symmetry property) Example: ⁵C₂ = ⁵C₃ = 10…
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