Permutations and Combination
Maharashtra Board · Class 11 · Mathematics & Statistics
Flashcards for Permutations and Combination — Maharashtra Board Class 11 Mathematics & Statistics. Quick Q&A cards covering key concepts, definitions, and formulas.
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What is the Addition Principle of counting? Give an example.
Answer
Addition Principle: If one operation can be done in m ways and another operation can be done in n ways, with no common way between them, then one of these operations can be performed in (m + n) ways.
What is the Multiplication Principle of counting? Solve: How many 3-digit numbers can be formed using digits 1,2,3,4,5 with repetition allowed?
Answer
Multiplication Principle: If one operation can be done in m ways, followed by another independent operation that can be done in n ways, then both operations can be performed in (m × n) ways. Solution…
Define factorial notation and calculate 6! and 0!
Answer
Factorial Notation: For natural number n, n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1 Calculations: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 0! = 1 (by definition) Key Properties: - n! = n × (n-1)! - n! is alw…
Solve: If (n+6)! = 56(n+4)!, find n.
Answer
Given: (n+6)! = 56(n+4)! Step 1: Expand (n+6)! (n+6)! = (n+6) × (n+5) × (n+4)! Step 2: Substitute in equation (n+6) × (n+5) × (n+4)! = 56 × (n+4)! Step 3: Cancel (n+4)! (n+6) × (n+5) = 56 Step 4: …
Define permutation and find the formula for ⁿPᵣ when all objects are distinct.
Answer
Permutation: An arrangement in definite order of a number of objects, taken some or all at a time. Formula: ⁿPᵣ = n!/(n-r)! Derivation: - 1st place: n choices - 2nd place: (n-1) choices - 3rd place:…
Solve: How many 4-digit numbers can be formed from digits 2,4,5,6,7 without repetition?
Answer
Step 1: Identify the problem type Arranging 4 digits from 5 available digits without repetition = ⁵P₄ Step 2: Apply formula ⁵P₄ = 5!/(5-4)! = 5!/1! = 5!/1 = 120 Step 3: Alternative calculation ⁵P₄ =…
When repetitions are allowed in permutations, what is the formula? Solve: How many 3-digit numbers can be formed from digits 1,2,3 with repetition?
Answer
Formula for permutations with repetition: Arranging n objects taken r at a time = nʳ Solution: Digits available: 1, 2, 3 (n = 3) Positions to fill: 3 (r = 3) Step 1: Each position can be filled inde…
How do you solve permutation problems when some objects are identical? Find arrangements of letters in 'GOOD'.
Answer
Formula for identical objects: If n objects have n₁ identical objects of type 1, n₂ identical objects of type 2, etc. Total arrangements = n!/(n₁! × n₂! × ... × nₖ!) Solution for 'GOOD': Step 1: Coun…
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