Combinatorics : relationship between Combinations and Permutations with similar objects I have a question in regards to relationship between Combinations and Permutations with like or repeated objects.
Using an example like the the word Mississipi, basic example of using Permutations with like letters.
I have seen this type done with multiplications of Combinations, which works out to be the Permutation formula with like elements which is = n!/a!b!c!, etc.
BUT there is also another formula for Combinations with Repititions, which is 
of the form : C(n+r-1, r).
Is there a relationship between all of these, this one an equivalent form of the above.
Also this "Combinations with Repetition" seems to even be similar to Binomial coefficients of Pascal Triangle.
SO just wondering if these are kind of one and the same structure, just 3 or 4 different forms of the same thing?
Hope someone can help.
P

The following are equivalent expressions for the multinomial coefficient:$${{}^{(a+b+c)}\mathrm C_{a,b,c}\\= \binom{a+b+c}{a,b,c}\\= \dfrac{(a+b+c)!}{a!~b!~c!}\\ = \binom{a+b+c}{a}\binom{b+c}b\\ \vdots \text{ and such like}}$$
The multinomial coefficient counts the ways to permute (or arrange) a multiset of $a, b,$ and $c$ items of three types (the items are otherwise considered indistinguishable).
This also counts the ways to select a combination of places for the items of each type. 
These are simply different ways of looking at the same task; the count of possible ways to perform them will therefore be the same.

The combination with repetition you mention counts ways to select a number of items from a set with replacement/repetition, when the order of selection is not recorded. (Each item may be selected multiple times.)
Choosing $k$ objects with repletion from a menu of $n$ can be counted as ways to arrange a string of $k$ 'stars' and $n-1$ 'bars', where the number of stars before the first bars counts the number of times the first object is selected, and so on, as though putting balls into boxes with the bars representing the dividers between boxes.  (This counting technique is thus known as "stars and bars")
Hence $\tfrac{(k+n-1)!}{k!~(n-1)!}$ is the count for ways to select with repetition, a combination of $k$ objects from a menu of $n$ .
