#### Permutations And Combinations

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, 08-14-2010 at 10:30 PM (1519 Views)
[QUOTE=suja84_ibt;205994]1. If one operation can be performed in m ways and another operation in n ways, then the two operations in succesion can be done in [b]m*n[/b] ways

2. The linear permutation of n [b]distinct[/b] objects (that is, the number of ways in which these n objects can be arranged is [b]n![/b] and the circular permutation of n distinct objects is [b](n-1)![/b] But if the clockwise and anticlockwise directions are indistinguishable then the circular permutations of n different things taken at a time is [b](n-1)!/2 [/b]

3. But out of these n objects, if there are n1 objects of a certain type, n2 of another type and n3 of another, and so on, Then the number of arrangements (linear permutations) possible is [b]n!/n1!n2!...nz![/b]

4. The total number of ways of arranging r things from n things is given by [b]nPr = n!/(n-r)!

[/b]5[b]. [/b]The number of ways to select r things out of n things is given by [b]nCr = n!/(r!*(n-r)!)

[/b]6[b]. nPr = r! * nCr [/b][/QUOTE]