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rajeshmarndi
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If we have n object and n1,n2,..nk are identical element. And we take r at a time i.e r < n. Is there a general formulae for the permutation of the above. Or how it is solved? Thanks.
A permutation of identical elements is a rearrangement of a set of elements where some or all of the elements are identical. This means that the order in which the elements appear is changed, but the elements themselves remain the same.
A permutation of identical elements involves rearranging the elements in a set, while a combination involves selecting a subset of elements from a larger set without rearranging them. In other words, a permutation changes the order of elements, while a combination does not.
The number of permutations of identical elements in a set can be calculated using the formula n! / (n1! * n2! * ... * nk!), where n is the total number of elements in the set and n1, n2, etc. represent the number of identical elements of each type. For example, a set with 4 elements, where 2 are identical, would have 4! / (2! * 1!) = 12 permutations.
Yes, a permutation of identical elements can result in the same set. This can happen when all the elements in the set are identical, as there is only one possible way to arrange them.
Permutations of identical elements are commonly used in statistics, probability, and cryptography. In real-life scenarios, they can be used to calculate the number of possible outcomes in a game, the number of unique passwords that can be created using a set of characters, or the number of ways a group of people can be seated at a table.