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PERMUTATIONS AND COMBINATIONS PermutationsThe number of ordered sequences where repetition is not allowed, ie no element can appear more than once in the sequence. Ordered samples (sequences) of size k from n nPk = n(n-1)(n-2)...(n-k+1) = n! / (n-k)! This is also known as the number of permutations of n distinct objects taken k at a time.
CombinationsThe number of unordered sets of distinct elements, ie repetition is not allowed. Number of ways of selecting k distinct elements from n or equivalently number of unordered samples of size k, without replacement from n nCk = nPk / k! = n! / k! (n-k)! This is the number of combinations of n distinct objects taken k at a time.
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