TERM RELATED TO PERMUTATIONS AND COMBINATIONS
AND ITS RELATED FORMULAS ,WHICH WE USE IN
OUR DAY TO DAY ACTIVITIES .
BASICS
1. WHAT IS A PERMUTATION ?
PERMUTATION :-
* PERMUTATION IS SIMPLY REFERED TO AS THE
ARRANGEMENT OF THINGS OR OBJECTS.
* THIS IS AS SHOWN IN BELOW FIGURE .
2. WHAT IS A COMBINATION ?
COMBINATION :-
* COMBINATION IS SIMPLY REFERED TO AS THE SELECTION
OF THINGS OR OBJECTS .
* THIS IS SHOWN IN BELOW FIGURE .
3. WHAT ARE THE TYPES OF PERMUTATIONS ?
TYPES OF PERMUTATIONS :-
* THERE ARE MAINLY TWO TYPES OF PERMUTATIONS .
* THEY ARE
(a) LINEAR PERMUTATION .
(b) CIRCULAR PERMUTATION .
* THESE ARE AS SHOWN IN BELOW FIGURE .
4. WHAT IS A LINEAR PERMUTATION ?
LINEAR PERMUTATION :-
LINEAR PERMUTATION IS A PERMUTATION WHERE THE
ARRANGEMENT OF THINGS ARE DONE IN A LINE (ROW) WISE .
5.WHAT IS A CIRCULAR PERMUTATION ?
CIRCULAR PERMUTATION :-
CIRCULAR PERMUTATION IS A PERMUTATION WHERE THE
ARRANGEMENT OF THINGS ARE DONE IN A CIRCLE WISE .
FORMULAS
LET US CONSIDER,
P= PRMUTATION ,
C= COMBINATION .
THEN,
1. nPr=P(n,r)=n!/(n-r)! = PERMUTATIONS FORMED BY
TAKING r THINGS FROM n DISSIMILAR THINGS .
2. nCr=C(n,r)=n!/((n-r)!r!) = COMBINATIONS FORMED BY
TAKING r THINGS FROM n DISSIMILAR THINGS.
3. n! = n*(n-1)*(n-2)*(n-3)....... .
4. C(n,r)+C(n,r-1)=C(n+1,r) .
5. C(n,r)/C(n,r-1)=(n-r+1)/r .
6. IF ONE WORK DONE IN m ROUTES ,OTHER IN n ROUTES
(BOTH ASSOCIATED ) ,THEN BOTH CAN BE DONE IN
SUCCESSION IN mn ROUTES.
7. THE ARRANGEMENT OF WAYS FOR n PENS n PENCILS ,
BOTH ALTERNATIVELY IN A LINE DONE IN 2 n! n! .
8. THE NUMBER OF CIRCULAR PERMUTATIONS FORMED BY
n DISSIMILAR THINGS IS (n-1)! .
9. THE POSSIBLE WAYS OF DISTRIBUTING n THINGS EQUALLY
AMONG 2 PERSONS IS (2n)!/(n!n!) .