Thread: STATISTICS, 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

Originally Posted by galaxie

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

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.