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

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

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;

nCr = n(n-1)(n-2)…(n-r+1)/ r! = n!/ r!(n-r)!= nPr /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 5nPr = nCr! ; if 0 < r ≤ n.

Theorem 6: nCnCr-1 = n+1Cr


Exe-8.1

 Permutations and Combinations ISC Class-11 Maths Ch-8


Exe-8.2

 Permutations and Combinations ISC Class-11 Maths Ch-8


Exe-8.3

Permutations and Combinations ISC Class-11 Math Ch-8


Exe-8.4

ML Aggarwal Permutations and Combinations


Exe-8.5

Permutations and Combinations ISC Class-11 Maths


Exe-8.6

ML Aggarwal ISC Class-11 Maths Ch-8


Exe-8.7

 Permutations and Combinations


Exe-8.8

ML Aggarwal Permutations and Combinations ISC Class-11


Chapter Test

 Permutations and Combinations

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4 thoughts on “Permutations and Combinations ISC Class-11 Maths ML Aggarwal”

  1. sir files are not opening sir
    problem to pahle se hi ithni hai life me aur ab apki site ne bhi saat chor diya
    sir jitni jaldi ho sake thik kariye varna annuals me acche no. nahi aayenge.
    please sir help the needy .

    Reply

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