# Permutation and Combination – Exercise 4.2 – Class X

Previous Exercise – Permutation and Combination – Exercise 4.1

#### Permutation and Combination – Exercise 4.2

1. Below are given situations for arrangements and selections. Classify them as examples of permutations and combinations.
2. A committee of 5 members to be chosen from a group of 12 people.
3. Five different subject books to be arranged on a shelf.
4. There are 8 chairs and 8 persons, a chairperson, a secretary and a treasure are to be chosen
5. In a committee of 7 persons, a chairperson, a secretary and a treasurer are to be chosen.
6. The number children’s clothing shop has 10 designs of frocks and 3 of them have to display in the front window.
7. Three letter words to be formed from the letters in the word ‘ARITHMETIC’.
8. In a question paper having 12 questions, students must answer the first 2 questions but may select any 8 of the remaining ones.
9. 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.
10. Three digit numbers are to be formed from the digits 1, 3, 5, 7, 9 where repetitions are not allowed.
11. Five keys are to be arranged in a circular key thing
12. 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.
13. A collection of 10 toys are to be divided equally between two children.

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

1. Below are given situations for arrangements and selections. Classify them as examples of permutations and combinations.
2. A committee of 5 members to be chosen from a group of 12 people.
3. Five different subject books to be arranged on a shelf.
4. There are 8 chairs and 8 persons, a chairperson, a secretary and a treasure are to be chosen
5. In a committee of 7 persons, a chairperson, a secretary and a treasurer are to be chosen.
6. The number children’s clothing shop has 10 designs of frocks and 3 of them have to display in the front window.
7. Three letter words to be formed from the letters in the word ‘ARITHMETIC’.
8. In a question paper having 12 questions, students must answer the first 2 questions but may select any 8 of the remaining ones.
9. 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.
10. Three digit numbers are to be formed from the digits 1, 3, 5, 7, 9 where repetitions are not allowed.
11. Five keys are to be arranged in a circular key thing
12. 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.
13. A collection of 10 toys are to be divided equally between two children.

Solution:

1. A committee of 5 members to be chosen from a group of 12 people – Example for Combination
2. Five different subject books to be arranged on a shelf. – Example for Permutation
3. There are 8 chairs and 8 persons, a chairperson, a secretary and a treasure are to be chosen – Example for Permutation
4. In a committee of 7 persons, a chairperson, a secretary and a treasurer are to be chosen. – Example for Combination
5. 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
6. Three letter words to be formed from the letters in the word ‘ARITHMETIC’. – Example for Permutation
7. 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
8. 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
9. Three digit numbers are to be formed from the digits 1, 3, 5, 7, 9 where repetitions are not allowed. – Example for Permutation
10. Five keys are to be arranged in a circular key thing – Example for Permutation
11. 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
12. A collection of 10 toys are to be divided equally between two children. – Example for Combination

Next exercise – Permutation and Combination – Exercise 4.3