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Saturday, 4 November 2017

Combinations

More Concepts and Formulas - CombinationsNumber of combinations of n distinct objects taking r at a time when each object may be repeated any number of times
(n+r-1)Cr
Number of ways in which one or more objects can be selected from n distinct objects (i.e., we can select 1 or 2 or 3 or … or n objects at a time)
nC1 + nC2 + ... + nCn = 2n - 1
Number of ways in which one or more objects can be selected out of S1 alike objects of one kind, S2 alike objects of second kind and S3 alike objects of third kind
= (S1 + 1)(S2 + 1)(S3 + 1) - 1
The above formula can be generalized as follows.
Number of ways in which one or more objects can be selected out of S1 alike objects of one kind, S2 alike objects of second kind , S3 alike objects of third kind and so on ... Sn alike objects of nth kind
= (S1 + 1) (S2 + 1)(S3 + 1)...(Sn + 1) - 1
Number of ways in which one or more objects can be selected out of S1 alike objects of one kind, S2 alike objects of second kind and rest p different objects
= (S1 + 1)(S2 + 1)2p - 1
The above formula can be generalized as follows.
Number of ways in which one or more objects can be selected out of S1 alike objects of one kind, S2 alike objects of second kind and so on ... Sn alike objects of nth kind and rest p different objects
= (S1 + 1) (S2 + 1) ... (Sn + 1) 2p - 1
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