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# Permutations And Combinations

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## Permutations And Combinations PDF Notes, Important Questions and Formulas

Introduction to permutations and combinations:

Permutations and Combinations:

 Permutations Combinations Arrangement in a definite. Order is considered Selection is made irrespective of arrangement Ordering of the objects is essential Ordering of the selected object is immaterial Permutation corresponds to only one combination Combination corresponds to many permutations Number of permutations exceeds the number of combinations Number of combinations is lesser than the number of permutations

FUNDAMENTAL PRINCIPLE OF COUNTING

Multiplication principle

If one operation can be performed in m ways and simultaneously another operation can be performed in n ways the number of ways of performing the two operations will be m × n.

FUNDAMENTAL PRINCIPLE OF ADDITION

If one operation can be performed in m-ways and another operation can be performed in n ways then either first or second operation can be happened in (m + n) ways.

Permutations (arrangements)

The number of permutations of n objects, taken r at a time is the total number of arrangements of ‘r’ objects taken from ‘n’ objects where order of arrangements matters. In other words it is total possible ordered sets of r elements selected from given ‘n’ elements.

A. Repetition is not allowed

(i) Number of ways in which n distinct object can be arranged amongst themselves is
= n . (n-1) (n-2) ................ 3.2.1 =m!

(ii) Number of ways in which we can arrange ‘n’ object taken r at a time B. Repetition is allowed.

The number of arrangements of n different objects, taken `r' at  a time, when each object may occur any number of  times ways.

Circular Permutation

The number of circular permutations of n different things taken all at a time is (n - 1)!
If clockwise & anti-clockwise circular permutations are considered to be same, the it is Show more

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