Class 12 Mathematics Permutation and Combination Notes has been updated according to the latest syllabus of 2080. It means the all the solutions of Class 12 Mathematics Combinations and Permutations chapter provided in this article contains all the new exercise that has recently been updated. Now you don’t need to go anywhere searching for the notes of permutations and combinations because we are here to serve you.

## Chapter – 1

__Permutation and Combination__

Permutation of a set of objects means an arrangement of objects in some order. Consider the numbers 456, 654. Both of them consist of the same digits 4, 5, 6. But they are arranged in different order. So they are different permutations of the digits 4, 5, 6. So we can form many different permutation from a given set of objects taken all at a time or taken particular number of objects at a time. The number of permutations that can be formed taken r at a time out of n given objects is given by the following theorem. We shall denote this number of permutations by P(n,r) or by nPr.

Class 12 Permutations and Combinations chapter has 3 exercises in total and in each exercise we will learn the method of finding combination and permutations. We have listed the notes of all exercises. You can click on the buttons given below to view exercise-wise notes.

### Permutation of objects not all different

To find the permutation of n objects taken all at a time when p of the objects are of first kind, q of them are of second kind, r of them are of the third kind and the rest all are different.Let the total number of permutations of n objects taken all at a time be x.

Out of these n objects, p of the objects of the first kind be replaced by p new objects different from one another and also different from each of the remaining objects. If these p different objects be arranged among themselves, keeping the positions of all other objects same, they will give p! permutations corresponding to each x permutations. Hence there will be x × p! permutations in all.

In the same way if q of the objects of the second kind be replaced by q new objects different from one another and from the remaining objects, in each of x × p! permutations, the total permutations is x × p!q! Similarly, if r of the objects be replaced by r different objects then we will have x × p!q!r! as the total number of permutations when all objects are different

## Class 12 Mathematics Permutation and Combination Notes PDF

This PDF will provide the solutions every question solutions for the 2nd exercise of class 12 permutation and combination chapter. If you want the solutions of other exercises then you can select the exercise from the button given below.

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### What does the solutions PDF contains?

In the first exercise of permutation and combination chapter there are 18 questions in total which needs to be solved by students. Some of them are given below. The question are very simple and students can easily solve them by looking at the examples given. Now talking about the solutions PDF, it contain the solutions of the questions given below.

- Find the number of permutations of five different objects taken three at a time.
- If three persons enter a bus in which there are ten vacant seats, find in how many ways they can sit?
- How many plates of vehicles consisting of 4 different digits can be made out of the integers 4, 5, 6, 7, 8, 9? How many of these numbers are divisible by 2?
- How many numbers of 4 different digit numbers can be formed from the digits 2, 3, 4,5, 6, 7? How many of these numbers are i) divisible by 5? ii) not divisible by 5?

- c) How many 5 digit odd numbers can be formed using the digits 3, 4, 5, 6, 7, 8 and 9. If
- repetition of digits is not allowed?
- repetition of digits is allowed?

- In how many ways can four boys and three girls be seated in a row containing seven seatsal
- If they may sit anywhere?
- If the boys and girls must alternate?
- If all three girls are together?
- If girls are to occupy odd seats?

- In how many ways can eight people be seated in a row of eight seats so that two particularpersons are
- Always together?
- Never together?

- Six different books are arranged on a shelf. Find the number of different ways in which the two particular books are;
- Always together
- Not together.

- In how many ways can four red beads, five white beads and three blue beads be arranged in a row?
- In how many ways can the letters of the following words be arranged?
- ELEMENT
- NOTATION
- MATHEMATICS
- MISSISSIPPI

- How many numbers of 6 digits can be formed with the digits 2, 3, 2, 0, 3, 3?

If you want to practice the questions without looking at the solutions PDF then you can definitely do that. It will help you to increase your knowledge and understanding. You can check your answer from the answers provided below. If you have done any mistakes then you can check the solutions PDF to know the right method of solving that problem.

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