# Combination usage in the well-known word problem

1. May 5, 2012

### 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?

2. May 5, 2012

### tiny-tim

Hi M. next!
"combination of k out of n", also written "n choose k", or nCk, 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

3. May 5, 2012

### D H

Staff Emeritus
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.

4. May 11, 2012

### M. next

oh thanks, and sorry for the late reply