**Previous Exercise – Permutation and Combination – Exercise 4.1 **

#### Permutation and Combination – Exercise 4.2

**Below are given situations for arrangements and selections. Classify them as examples of permutations and combinations.**- A committee of 5 members to be chosen from a group of 12 people.
- Five different subject books to be arranged on a shelf.
- There are 8 chairs and 8 persons, a chairperson, a secretary and a treasure are to be chosen
- In a committee of 7 persons, a chairperson, a secretary and a treasurer are to be chosen.
- The number children’s clothing shop has 10 designs of frocks and 3 of them have to display in the front window.
- Three letter words to be formed from the letters in the word ‘ARITHMETIC’.
- In a question paper having 12 questions, students must answer the first 2 questions but may select any 8 of the remaining ones.
- A jar contains 5 black and 7 white balls. 3 balls to be drawn in such a way that 2 are black and 1 is white.
- Three digit numbers are to be formed from the digits 1, 3, 5, 7, 9 where repetitions are not allowed.
- Five keys are to be arranged in a circular key thing
- There are 7 points in a plane and no 3 of the points are colinear. Triangles are to be drawn by joining three non colinear points.
- A collection of 10 toys are to be divided equally between two children.

#### Permutation and Combination – Exercise 4.2 – Solutions:

**Below are given situations for arrangements and selections. Classify them as examples of permutations and combinations.****A committee of 5 members to be chosen from a group of 12 people.****Five different subject books to be arranged on a shelf.****There are 8 chairs and 8 persons, a chairperson, a secretary and a treasure are to be chosen****In a committee of 7 persons, a chairperson, a secretary and a treasurer are to be chosen.****The number children’s clothing shop has 10 designs of frocks and 3 of them have to display in the front window.****Three letter words to be formed from the letters in the word ‘ARITHMETIC’.****In a question paper having 12 questions, students must answer the first 2 questions but may select any 8 of the remaining ones.****A jar contains 5 black and 7 white balls. 3 balls to be drawn in such a way that 2 are black and 1 is white.****Three digit numbers are to be formed from the digits 1, 3, 5, 7, 9 where repetitions are not allowed.****Five keys are to be arranged in a circular key thing****There are 7 points in a plane and no 3 of the points are colinear. Triangles are to be drawn by joining three non colinear points.****A collection of 10 toys are to be divided equally between two children.**

Solution:

- A committee of 5 members to be chosen from a group of 12 people –
**Example for Combination** - Five different subject books to be arranged on a shelf. –
**Example for Permutation** - There are 8 chairs and 8 persons, a chairperson, a secretary and a treasure are to be chosen –
**Example for Permutation** - In a committee of 7 persons, a chairperson, a secretary and a treasurer are to be chosen. –
**Example for Combination** - The number children’s clothing shop has 10 designs of frocks and 3 of them have to display in the front window. –
**Example for Permutation** - Three letter words to be formed from the letters in the word ‘ARITHMETIC’. –
**Example for Permutation** - In a question paper having 12 questions, students must answer the first 2 questions but may select any 8 of the remaining ones. –
**Example for Combination** - A jar contains 5 black and 7 white balls. 3 balls to be drawn in such a way that 2 are black and 1 is white. –
**Example for Combination** - Three digit numbers are to be formed from the digits 1, 3, 5, 7, 9 where repetitions are not allowed. –
**Example for Permutation** - Five keys are to be arranged in a circular key thing –
**Example for Permutation** - There are 7 points in a plane and no 3 of the points are colinear. Triangles are to be drawn by joining three non colinear points. –
**Example for Combination** - A collection of 10 toys are to be divided equally between two children. –
**Example for Combination**

**Next exercise – ****Permutation and Combination – Exercise 4.3**