Combination usage in the well-known word problem

[M. next]

How many different letter arrangement can be made from the 11 letters of MISSISSIPPI?

(But using COMBINATION not the different permutation method)

I saw an answer and it says:
(combination of 1 out of 11)*(combination of 4 out of 10)*(combination of 4 out of 6) *(combination of 2 out of 2)

What does combination exactly mean, and in what way was it used here?

I mean if we don't want same words to appear, what will this have to do with taking say 4 Ss out of the left 10?

Thanks in advance.

 

[tiny-tim]

Hi M. next!

What does combination exactly mean, and in what way was it used here?

I mean if we don't want same words to appear, what will this have to do with taking say 4 Ss out of the left 10?

"combination of k out of n", also written "n choose k", or ⁿC_k, or the vertical matrix (n k), and equal to n!/k!(n-k)!,

is the number of ways of selecting k things out of n where the order does not matter

see http://www.mathsisfun.com/combinatorics/combinations-permutations.html for details ​

 

[D H]

(But using COMBINATION not the different permutation method)

I saw an answer and it says:
(combination of 1 out of 11)*(combination of 4 out of 10)*(combination of 4 out of 6) *(combination of 2 out of 2)Thanks in advance.

That's the answer for the number of permutations, not the number of combinations.

The difference between the two: "issi" and "siis" are two different permutations (arrangements) of the letters i,i,s, and s. They are not different combinations, however; order doesn't matter in combinations.

Suppose we put labels on the duplicated letters, making mississippi become mi₁s₁s₂i₂p₁p₂i₃s₃s₄i₄. There are 11 factorial (11!) permutations of these labeled letters because each (labeled) letter is distinct. For example, i₁s₁s₂i₂ and i₁s₁s₃i₂ are distinct permutations. Take those labels away and these two permutations become issi and issi: they are now indistinguishable.

The problem is to find the number of distinguishable permutations of the given (unlabeled) letters.

 

[M. next]

oh thanks, and sorry for the late reply