How many different 5-letter "words" can be formed from the 10 letters in STATISTICS?

10 letter "words" is okay 10!/(3!3!2!). Do we have to look at all the cases here. ie with a,c and without including various of s,t,i to make up the 5.??

Any ideas

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- May 12th 2008, 02:36 AMgalaxieSTATISTICS, how many 5-letter arrangements?
How many different 5-letter "words" can be formed from the 10 letters in STATISTICS?

10 letter "words" is okay 10!/(3!3!2!). Do we have to look at all the cases here. ie with a,c and without including various of s,t,i to make up the 5.??

Any ideas - May 12th 2008, 09:54 AMPlato
**This is just a tedious problem with no simple approach.**

To solve it you must consider all possible cases.

The first case is with no letter repeated: (5!)

Then you might consider “words” with 2 or 3 S’s but on other repeats.

Double that to account for similar cases using T’s.

The another case would be: 2 S’s , 2 T’s and another.

As you can see it is messy to find all cases.

Good Luck.