Download NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations क्रमचय और संचय free in PDF form for CBSE, Uttarakhand Board, Bihar Board, UP Board and other state board’s students, who are following NCERT Books for their school exams. Students can do directly class 12 without appearing in 11th through NIOS Online Admission. It is equally valuable as the other boards.
NCERT Solutions for Class 11 Maths Chapter 7
Class 11 Maths Chapter 7 Permutations & Combinations Solutions
- Download Exercise 7.1
- Download Exercise 7.2
- Download Exercise 7.3
- Download Exercise 7.4
- Download Miscellaneous Exercise 7
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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).