## 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?