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 “ ^{n}P_{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;

_{n}C_{r} = n(n-1)(n-2)…(n-r+1)/ r! = n!/ r!(n-r)!= _{n}P_{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**: ^{n}P_{r} = ^{n}C_{r }r! ; if 0 < r ≤ n.

**Theorem 6: ^{n}**C

_{r }+

^{n}C

_{r-1}=

^{n+1}C

_{r}

**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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re appear soon

sir files are not opening sir

problem to pahle se hi ithni hai life me aur ab apki site ne bhi saat chor diya

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sure