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NCERT Solutions for Class 11 Math Ch-6: Permutations and Combinations
NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations covers the fundamental principle of counting, factorial notation, and the formulas for calculating permutations and combinations of objects.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: State the fundamental principle of counting.
Answer: The fundamental principle of counting states that if an event can occur in 'm' different ways, and following it, a second event can occur in 'n' different ways, then the two events together can occur in m × n different ways.
Q2: What is a permutation, and what is the formula for nPr?
Answer: A permutation is an arrangement of a certain number of objects taken from a larger group, where the order of arrangement matters. The formula for the number of permutations of n distinct objects taken r at a time is nPr = n! / (n − r)!.
Q3: What is a combination, and what is the formula for nCr?
Answer: A combination is a selection of a certain number of objects from a larger group, where the order of selection does not matter. The formula for the number of combinations of n distinct objects taken r at a time is nCr = n! / [r!(n − r)!].
Q4: What is the key difference between a permutation and a combination?
Answer: The key difference is that in permutations, the order of arrangement of objects matters (e.g., arranging books on a shelf), whereas in combinations, only the selection of objects matters and order is irrelevant (e.g., choosing a committee of people).
Q5: What is the value of 0! (zero factorial), and why is it defined this way?
Answer: The value of 0! is defined as 1. This convention is adopted so that formulas involving factorials, such as those for permutations and combinations, remain consistent and valid even when r = 0 or r = n.
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