Permutations with Repetition and Repeated Elements

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SUMMARY

The discussion clarifies the mathematical principles of permutations with repetition and repeated elements. It establishes that for x objects with a repetitions of one element and b repetitions of another, the formula for permutations without repetition is given by Np(without repetition) = x!/(a!b!). When repetitions are allowed, the formula changes to Np(with repetition) = x^x. The combined formula for permutations with repetition and repeated elements is Np(with repetition) = x^x/(a!b!). These formulas are essential for accurately calculating permutations in combinatorial problems.

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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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