# ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding

ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding 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.

## ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Class: | 11th |

Subject: | Mathematics |

Chapter : | Ch-8 Permutations and Combinations of Section -A |

Board | ISC |

Writer | ML Aggarwal |

Publications | APC Arya Publications 2020-21 |

**-: Select Topics :- **

## ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

**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.

**Fundamental Principles of Counting**

**Multiplication Principle:** Suppose an operation A can be performed in m ways and associated with each way of performing of A, another operation B can be performed in n ways, then total number of performance of two operations in the given order is mxn ways. This can be extended to any finite number of operations.

**Addition Principle:** If an operation A can be performed in m ways and another operation S, which is independent of A, can be performed in n ways, then A and B can performed in (m + n) ways. This can be extended to any finite number of exclusive events.

**Factorial**

The continued product of first n natural number is called factorial ‘n’.

It is denoted by n! or n! = n(n – 1)(n – 2)… 3 × 2 × 1 and 0! = 1! = 1

**Permutation**

Each of the different arrangement which can be made by taking some or all of a number of objects is called permutation.

**Combination**

Each of the different groups or selections which can be made by some or all of a number of given things without reference to the order of the

things in each group is called a combination.

**Exe-8.1**

### ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

Find the value of :

(i) ………….

(ii) …………..

(iii) ……………

(iv) …………..

(v) …………

(vi) ……….

(vii) ……….

(viii) ……

(ix) ……….

Question 2:

………………….

…………………..

…………………..

Question 7:

Find the value of n, if

(i) ………….

(ii) …………..

(iii) ……………

(iv) …………..

(v) …………

**Exe-8.2**

### Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

(i) In a cricket match ………….. of the match.

(ii) In a class there ………………. make this selection ?

Question 2:

…………………..

………………….

…………………..

Question 25:

How many odd number less than 1000 can be formed using the digit 0, 4, 5, 7, if

(i) repetition of digits is allowed ?

(ii) repetition of digits is not allowed ?

**Exe-8.3**

Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

Find the value of

(i) p (4,3)

(ii)P(65, 2)

……………….

Question 2:

Prove that

(i)……….

(ii)………..

(iii)……….

Question 3:

…………………….

………………….

………………………

Question 32:

There are 3 candidate ………………… vote are possible ?

**Exe-8.4**

ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

In ow many ways can 3 white, ………………….. colure are indistinguishable ?

Question 2:

In how many ways can 4 ……………………………… colure are indistinguishable ?

Question 3:

……………………….

…………………………

………………………….

Question 12:

How many arrangement can be made with the letters of the word MATHEMATIC if

(i) …………….

(ii)……………..

(iii)…………..

……………….

**Exe-8.5**

### Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

In how many ways can four persons A, B, C and D be seated at a circular table ?

Question 2:

In how many …………………… circular table ?

Question 3:

…………………..

…………………….

……………………..

Question 11:

Indian cricket team sits down for dinner at a round table . In how many arrangement is Virat flanked by Rohit and Dhawan ?

**Exe-8.6**

### ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

Evaluate the following :

(i)…………..

(ii)………..

(iii)……………

Question 2:

…………………..

…………………….

………………………

Question 29:

How many 4-letter words can be formed from the letter of the word “COMBINATION” ?

**Exe-8.7**

Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

(I) A man has 5 ………………………………. friends to a dinner ?

(ii) In order to pass an ………………………….. can a student fail?

Question 2:

From 4 mangoes, 5 oranges and …………………. at least one of them ?

Question 3:

……………………

…………………….

……………………..

Question 9:

(i) What is the number of ways of ……………. beggars ?

(ii) What is the number ……………… 5 person ?

(iii) What is the number …………………….. remains empty ?

**Exe-8.8**

ML Aggarwal Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

Prove that ……………. divides |_ 30?

Question 2:

If r ≤ s ≤ n …………… by (n, r).

Question 3:

…………………….

…………………….

…………………….

Question 21 :

If all letters of the word ” ZENITH ” are written in all possible ……………………. rank of the word zenith.

**Chapter Test**

### Permutations and Combinations ISC Class-11 Maths Understanding Ch-8

Question 1:

The digits, 0 to 9 , are ………….. outcomes are possible ?

Question 2:

There are 6 items ………………….. to the question ?

Question 3:

……………………

……………………

…………………….

Question 16:

How many word can be formed by ………………. of the word “MATHEMATIC” ?

-: End of Permutations and Combinations ISC Class-11 ML Aggarwal Maths Understanding Chapter-8 Solution :-

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