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Introduction to permutations and combinations:
Permutations and 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
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.
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.
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
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