Permutations and Combinations
Posted by
Ravi Kumar at Monday, November 24, 2008
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Permutations and Combinations
Permutations and Combinations
Formulae:
Factorial Notation:
Let n be positive integer.Then ,factorial n dentoed by n!
is defined as n! = n(n1)(n2). . . . . . . .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(n1)(n2). . .. . . (nr+1)
= n! / (nr)!
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!)