# CombinationsÂ

ÂGroups or selections are called combinations

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The number of combination of n different things taken r at a time is

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Combination of n different things taking some or all of n things at a time is-

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Â Â Â Â Â 2^{n} â€“ 1

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The combinations of selecting r_{1}Â things from a set having n_{1}, objects and r_{2} things from a set having n_{2} objects where combination of r_{1} things, r_{2} things are independent is given by

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**Cor. 1Â Â **The number of ways in which (p + q + r) things can be arranged into three groups containing p, q and r things respectively is

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**Cor.2Â Â Â **The number of ways in which 3p things can be divided equally into three distinct groups is

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**Cor.3Â Â **The number of ways in which 3p things can be divided equally into three persons is

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