combinatorics – k-permutations of NON DISTINCT elements for example the word ‘Mississippi’

I’m a little bit confused about permutation. Consider the string Mississippi. I need a k-permutation without repetition of the string. I know that Misp is a compatible k-permutation. However, is Mispp a good one? On one hand it is not, because p in Mispp is shown twice. On the other hand, it is, because the original Mississippi contains p twice, so each of the p is shown only once.

Same with n-permutation without repetition. Is pipiMissssi a “permutation without repetition” of the original word?

combinatorics – A simpler approach to solve “how many k-permutations of aaabbccdef are there?”

Given a problem as follows.

How many 4-permutations of “aaabbccdef” are there?

Divide the problem into disjoint cases:

  • 4-permutation of ${a,b,c,d,e,f}$
  • permutation of ${2*x, y, z}$
  • permutation of ${2*x, 2*y}$
  • permutation of ${3*a, x}$

The number of permutations for

  • case 1: $P^6_4=360$
  • case 2: $C^3_1times C^5_2timesfrac{4!}{2!}=360$
  • case 3: $C^3_2times frac{4!}{2!times 2!}=18$
  • case 4: $C^5_1times frac{4!}{3!}=20$

Total number of permutation is $758$.

Is there any simpler approach which is very useful for longer words to be made?