Class 11 Maths Chapter 7 Notes
Important Complete Class 11 Maths Chapter 7 Notes written by Professor M. Asad Khalid Suib. These notes are very helpful in the preparation of Permutation Combination and Probability Pdf for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Definition of factorial with its notation and examples
- Our comprehensive Class 11 Maths Chapter 7 Notes will ensure you're fully prepared for your exams.
- Solution of each question of Exercise 7.1 in the 1st year Mathematics of the Punjab Textbook Boards.
- Definition of a permutation and Proofs.
- Fundamental principle of continuity
- Solution of each question of Exercise 7.2 in the 1st year Mathematics of the Punjab Textbook Boards.
- Solution of each question of Exercise 7.3 in the 1st year Mathematics of the Punjab Textbook Boards.
- Solution of each question of Exercise 7.4 in the 1st year Mathematics of the Punjab Textbook Boards.
- Definition of probability, sample space, and event.
- Solution of each question of Exercise 7.5 in the 1st year Mathematics of the Punjab Textbook Boards.
- Example 3: In how many ways can a set of 4 diferent mathematics books and 5 diferent physics books be placed on a shelf with a space for 9 books, if all books on the same subject are kept together? Solution: 4 diferent Mathematics books can be arranged among themselves in 4! ways. 5 diferent Physics books can be arranged among themselves in 5! ways.To every one way of arranging 4 mathematics books there are 5! ways of arranging 5 physics books. The books in the two subjects can be arranged subject-wise in 2! ways.
- Find the number of 5-digit numbers that can be formed from the digits 1, 2, 4, 6, 8 (when no digit is repeated), but i) the digits 2 and 8 are next to each other; ii) the digits 2 and 8 are not next to each other.
- How many 6-digit numbers can be formed, without repeating any digit from the digits 0, 1, 2, 3, 4, 5? In how many of them will 0 be at the tens place?
- How many 5-digit multiples of 5 can be formed from the digits 2, 3, 5, 7,9, when no digit is repeated.
- In how many ways can 8 books including 2 on English be arranged on a shelf in such a way that the English books are never together?
- Find the number of arrangements of 3 books on English and 5 books on Urdu for placing them on a shelf such that the books on the same subject are together.
- In how many ways can 5 boys and 4 girls be seated on a bench so that the girls and the boys occupy alternate seats?
- How many arrangements of the letters of the following words, taken all together, can be made: i) PAKPATTAN ii) PAKISTAN ii) MATHEMATICS iv) ASSASSINATION?
- How many permutation of the letters of the word PANAMA can be made, if P is to be the irst letter in each arrangement?
- How many arrangements of the letters of the word ATTACKED can be made, if each arrangement begins with C and ends with K?
- How many numbers greater than 1000,000 can be formed from the digits 0, 2, 2,2, 3, 4 ,4 ?
- How many 6-digit numbers can be formed from the digits 2, 2, 3, 3, 4, 4? How many of them will lie between 400,000 and 430,000?
- 11 members of a club form 4 committees of 3, 4, 2, 2 members so that no member is a member of more than one committee. Find the number of committees.
- The D.C.Os of 11 districts meet to discuss the law and order situation in their districts. In how many ways can they be seated at a round table, when two particular D.C.Os insist on sitting together?
- The Governor of the Punjab calls a meeting of 12 oicers. In how many ways can they be seated at a round table?