Class 11 Maths - ODISHA
Permutations and Combinations
The chapter Permutations and Combinations in Class 11 Mathematics for the Odisha (BSE) board introduces fundamental counting principles that help determine the number of ways objects can be arranged or selected. You will learn the difference between permutations, where order matters, and combinations, where order does not matter. This chapter builds a strong foundation for understanding probability, binomial theorem, and higher-level algebra. Scoring well in this chapter is crucial for board exams as it features regularly in both short-answer and long-answer sections, testing your logical thinking and application of formulas.
Start Learning FreeKey Concepts
Fundamental Principle of Counting
If an event can occur in m different ways and a second event can occur in n different ways, then the two events together can occur in m times n ways (Multiplication Principle).
Factorial Notation
The product of all positive integers less than or equal to a given positive integer n, denoted by n! or factorial n.
Permutation
An arrangement of a set of objects in a specific order, calculated as nPr = n! / (n-r)!.
Combination
A selection of items from a larger collection where the order of selection does not matter, calculated as nCr = n! / [r! (n-r)!].
Relation between Permutation and Combination
The connection between selections and arrangements, expressed mathematically as nPr = nCr * r!.
Important Formulas
Board Exam Info
In the Odisha (BSE) Class 11 Mathematics board examinations, this chapter typically carries around 8 to 12 marks. Common question types include word problems based on seating arrangements, word formation, team selection, and direct evaluation or proving identities involving nPr and nCr.
Frequently Asked Questions
How do I know whether to use permutation or combination in a word problem?
Ask yourself if the order of items matters. If rearranging the chosen items creates a different outcome (like passwords or seating), use permutation. If order does not matter (like forming a committee or card hands), use combination.
What is the value of 0!?
By definition and mathematical convention, 0! (zero factorial) is always equal to 1, which helps keep formulas for permutations and combinations valid when r equals n or 0.
Can r be greater than n in nPr or nCr?
No, r can never be greater than n because you cannot select or arrange more items than are actually available in the given set.
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