Permutations with Repetition and Repeated Elements

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The discussion centers on the formulas for permutations with and without repetition. For Np without repetition, the formula is x!/(a!b!), where x is the total number of objects and a and b are the counts of repeated elements. When repetitions are allowed, the formula changes to Np with repetition = x^x. The combined formula for permutations with repetition, considering repeated elements, is Np = x^x/(a!b!). The conversation highlights the complexity of these concepts and suggests external resources for further clarification.
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The theory says that if you have x objects containing a repeats of one element and b repeats of another, Np(without repetition)=x!/(a!b!).

If you have x objects and repetitions are allowed, Np(with repetition)=xx, correct?

Combining these, if we have x objects containing a repeats of one element and b repeats of another, and repetitions are allowed, Np(with repetition)=xx/(a!b!). Is this right?
 
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