Permutations and Combinations ISC Class-11 Maths ML Aggarwal

Permutations and Combinations ISC Class-11 Maths ML Aggarwal Solutions Chapter-8. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe-1,  Exe-2, Exe-3, Exe-4, Exe-5, Exe-6, Exe-7, Exe-8, and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

Permutations and Combinations ISC Class-11 Maths ML Aggarwal

Board	ISC
Class	11
Subject	Mathematics
Chapter-8	Permutations and Combinations
Session	2024-25
Topics	Solutions of ML Aggarwal

Permutations and Combinations

If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m × n.”

“If an event can occur in m different ways, following which another event can occur in n different ways, following which a third event can occur in p different ways, then the total number of occurrence to ‘the events in the given order is m × n × p.”

Permutation Definition

A permutation is defined as an arrangement in a definite order of a number of objects taken, some or all at a time. Counting permutations are merely counting the number of ways in which some or all objects at a time are rearranged. The convenient expression to denote permutation is defined as “ ⁿP_r ”

Factorial notation 

The notation n! represents the product of first n natural numbers, i.e., the product 1 × 2 × 3 × . . . × (n – 1) × n is denoted as n!. We read this symbol as ‘n factorial’.

Thus, 1 × 2 × 3 × 4 . . . × (n – 1) × n = n !

Combination Definition

The combination is a selection of a part of a set of objects or a selection of all objects when the order doesn’t matter. Therefore, the number of combinations of n objects taken r at a time and the combination formula is given by;

_nC_r = n(n-1)(n-2)…(n-r+1)/ r! = n!/ r!(n-r)!= _nP_r /r!

Relationship Between Permutation and combination

In permutation and combination for class 11, the relationship between the two concepts is given by two theorems. They are;

Theorem 5: ⁿP_r = ⁿC_r r! ; if 0 < r ≤ n.

Theorem 6: ⁿC_r + ⁿC_r-1 = ⁿ⁺¹C_r

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Exe-8.1

 Permutations and Combinations ISC Class-11 Maths Ch-8

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Exe-8.2

 Permutations and Combinations ISC Class-11 Maths Ch-8

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Exe-8.3

Permutations and Combinations ISC Class-11 Math Ch-8

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Exe-8.4

ML Aggarwal Permutations and Combinations

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Exe-8.5

Permutations and Combinations ISC Class-11 Maths

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Exe-8.6

ML Aggarwal ISC Class-11 Maths Ch-8

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Exe-8.7

 Permutations and Combinations

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Exe-8.8

ML Aggarwal Permutations and Combinations ISC Class-11

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Chapter Test

 Permutations and Combinations

-: End of Permutations and Combinations ISC Class-11 ML Aggarwal Maths  :-

Return to :-  ML Aggrawal ISC Class-11 Maths Vol-1 Solutions

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