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how to derive the permutation formula. The proof is completed. It is clear that all these permutations are different and any possible permutation is covered in this way.
Permutation n P r n nr. A permutation is the arrangements of r things from a set of n things without replacement. Therefore P n n.
Now when there are more than one type of indistinguishable object then the only thing that changes is the way you calculate the number of permutations per distinct permutation.
It is clear that all these permutations are different and any possible permutation is covered in this way. C n r r. Use The Multiplication Rule To Show That This Is Indeed The Case. According to the formula on the number of permutations see the lessons Introduction to Permutations.