# Permutations

ÂArrangements are called permutations.

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

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Using factorial notations

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Number of permutations of n things, taken all a time, of which p are alike of one kind, q are alike of 2^{nd} kind, r are alike of third kind and rest are different

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# Circular Permutations

Â(i)Â The number of circular permutations of n objects = (n â€“ 1)! Because in a circular permutation one thing is kept fixed and the remaining (n â€“ 1) things are arranged in (n â€“ 1)! Ways. Â

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(ii)Â If the clockwise and anticlockwise orders are not distinguishable, then the number of ways = Â Â Â Â Â Â

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# Permutation with restrictions

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Permutation of n different things when a particular object is not taken in any arrangements is

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Permutation of n different things when a particular object is always included in any arrangements is

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