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CBSE Guide Permutations And Combinations class 11 Notes

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Permutations And Combinations class 11 Notes Mathematics

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CBSE Class 11 Mathematics
Revision Notes
Chapter-7
Permutations and Combinations

1. Fundamental Principle of Counting
2. Permutations
3. Combinations

Fundamental Principle of Counting

• Addition Law: If there are two operations such that such that they can be performed independently in  and  ways respectively, then either of the two operations can be performed in  ways.
• Multiplication: If one operation can be performed in  ways and if corresponding to each of the  ways of performing this operation, there are  ways of performing a second operation, then the number of ways of performing two operations together in .
• Factorial Notation: The continued product of first  natural numbers is called the ‘ factorial’ and is denoted by .
• 
• Permutations: The number of permutations of n different things taken r at a time, where repetition is not allowed, is denoted by  and is given by

• The number of permutations of n different things, taken r at a time, where repeatition is allowed, is .

• The number of permutations of  n objects taken all at a time, where   object are of first kind,  objects are of the second kind, …, objects are of the  kind and rest, if any, are all different is

Combinations:

• The number of combinations of n different things taken r at a time, denoted by  is given by
• 
• 
• 
• 
• 
• 
• Division into Groups: The number of ways  things can be divided into two groups containing  and  things respectively =

The Permutations And Combinations class 11 Notes

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