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## NCERT Solutions for Class 11 Maths Chapter 7

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### Class 11 Maths Chapter 7 Permutations & Combinations Solutions

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#### Important Terms on Permutations & Combinations

*Permutation*: A permutation is an arrangement of a number of objects in a definite order taken some or all at a time.*Combination*: Each of the different selections made by choosing some or all of a number of objects, without considering their order is called a combination. The number of combination of n objects taken r at a time where 0 ≤ r ≤ n, is denoted by nCr or C(n, r).*Multiplication Principle*(Fundamental Principle of Counting): If an event can occur in m different ways, following which another event can occur in n different ways, then the total no. of different ways of occurrence of the two events in order is m × n.*Factorial*: Factorial of a natural number n, denoted by n! or n is the continued product of first n natural numbers. n! = n × (n – 1) × (n – 2) × … × 3 × 2 × 1 or equal to n × ((n – 1)!) or equal to n × (n – 1) × ((n – 2)!)*Fundamental Principle of Addition*: If there are two events such that they can occur independently in m and n different ways respectively, then either of the two events can occur in (m + n) ways.- The number of permutation of n different objects taken r at a time where 0 ≤ r ≤ n and the objects do not repeat is denoted by nPr or P(n, r).