## Unit 06: Permutation, Combination and Probability (Solutions)

This is a sixth unit of the book Mathematics 11 published by Khyber Pakhtunkhwa Textbook Board, Peshawar, Pakistan. On this page we have provided the solutions of the questions.

After reading this unit the students will be able to

- Know Kramp's factorial notation to express the product of first $n$ natural numbers by $n!$
- Recognize the fundamental principle of counting and illustrate this principle using tree diagram.
- Explain the meaning of permutation of $n$ different objects taken $r$ at a time and know the notation.
- Apply $^nP_r$ to solve relevant problems of finding the number of an arrangement of $n$ objects taken $r$ at a time (when all n objects are different and when some of them are alike).
- Find the arrangement of different objects around a circle.
- Define combination of $n$ different objects taken $r$ at a time.
- Solve problems involving combination.
- Define the following:
- statistical experiment,
- sample space and an event,
- mutually exclusive events,
- equally likely events,
- dependent and independent events,
- simple and compound events.
- Apply the formula for finding probability in simple cases.
- Use Venn diagrams and tree- diagrams to find the probability for the occurrence of an event.
- Define the conditional probability
- Recognize the addition theorem ( or law) of probability.
- Recognize multiplication theorem (or law) o probability.
- Use theorem of addition and multiplication of probability to solve related problems.