Permutation & Combination's Formula:-
-> Factorial Notation :- Let n be positive integer.Then ,factorial n
dentoed by n! is defined as
n! = n(n-1)(n-2). . . . . . . .3.2.1
eg:- 5! = (5 * 4* 3 * 2 * 1)
= 120
0! = 1
->Permutations :- The different arrangements of a given number of things by taking some or all at a time,are called permutations.
eg:- All permutations( or arrangements)made with the letters a,b,c by
taking two at a time are (ab,ba,ac,ca,bc,cb)
->Numbers of permutations :- Number of all permutations of n things, taken r at a time is given by
nPr = n(n-1)(n-2). . .. . . (n-r+1)
= n! / (n-r)!
->An Important Result :- If there are n objects of which p1 are alike of one kind; p2 are alike of another kind; p3 are alike of third kind and so on and pr are alike of rth kind, such that (p1+p2+. . . . . . . . pr) = n
Then,number of permutations of these n objects is:
n! / (p1!).(p2!). . . . .(pr!)
->Combinations :- Each of different groups or selections which can be
formed by taking some or all of a number of objects,is called a
combination.
eg:- Suppose we want to select two out of three boys A,B,C .
then, possible selection are AB, BC & CA.
Note that AB and BA represent the same selection.
-> Number of Combination :- The number of all combination of n things taken r at atime is:
nCr = n! / (r!)(n-r)!
= n(n-1)(n-2). . . . . . . tor factors / r!
Note: nCn = 1 and nC0 = 1
An Important Result : nCr = nC(n-r)
