PERMUTATIONS
Explain Permutation.
Let y be non−empty se t . A bijective mapping β : y → yis called permutation on y .
Now will have to discuss Identity Permutations;
Let y be non –empty set. A bijective mapping β : y → yis called identity permutation on y ,if
d(y)=y { y=1,2,3 , … … }
For example
d(1)=1 {d (1 ) d 12( 2) d3(43) d ( 4)}
d(2)=2 {1212 33 44 }
d(3)=3
d(4)=4
Remark: If y has n elements, then total numbers of permutation on y is n!.
For example , y={ 2 } so n=1 then total permutation on y = n!
=1!=1
{22}
Example : 02
y={ 1,2,3,4 } so n=4 then total permutations on y =n !
4!=4.3.2.1=24
Explain Permutation.
Let y be non−empty se t . A bijective mapping β : y → yis called permutation on y .
Now will have to discuss Identity Permutations;
Let y be non –empty set. A bijective mapping β : y → yis called identity permutation on y ,if
d(y)=y { y=1,2,3 , … … }
For example
d(1)=1 {d (1 ) d 12( 2) d3(43) d ( 4)}
d(2)=2 {1212 33 44 }
d(3)=3
d(4)=4
Remark: If y has n elements, then total numbers of permutation on y is n!.
For example , y={ 2 } so n=1 then total permutation on y = n!
=1!=1
{22}
Example : 02
y={ 1,2,3,4 } so n=4 then total permutations on y =n !
4!=4.3.2.1=24
