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Combination usage in the wellknown word problemby M. next
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#1
May512, 09:36 AM

P: 378

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. 


#2
May512, 12:56 PM

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P: 26,148

Hi M. next!
is the number of ways of selecting k things out of n where the order does not matter see http://www.mathsisfun.com/combinator...mutations.html for details 


#3
May512, 01:52 PM

Mentor
P: 15,147

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 mi_{1}s_{1}s_{2}i_{2}p_{1}p_{2}i_{3}s_{3}s_{4}i_{4}. There are 11 factorial (11!) permutations of these labeled letters because each (labeled) letter is distinct. For example, i_{1}s_{1}s_{2}i_{2} and i_{1}s_{1}s_{3}i_{2} 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. 


#4
May1112, 10:48 AM

P: 378

Combination usage in the wellknown word problem
oh thanks, and sorry for the late reply



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