This is very atypical of questions on the test and it's likely you won't have more than one combination / permutation question on the entire test. Just FYI - you may not be using your time wisely by getting this deeply into this topic.
The basic "how many ways can I write the letters in THIS WORD" problem assumes that we are using all of the letters and that the order matters - and there is a formula for this type of problem (see below). The problem posted above adds a restriction that we can't use all of the letters. I've never seen a problem of the first type on the test, let alone the FAR more complicated type posted above. There are probably formulas for those, too, but I don't know what they are - and you don't need to know them for the test. (But if you still want to know - does anyone else know?)
For basic problems of this type, the formula is:
n! / (r1!r2!r3!...)
where n represents the total number of letters and r1, r2, etc, represent the number of letters for every letter you have. So for "Tennessee" we'd have:
9! / (1!4!2!2!)
or 3,780 options (again, using all 9 letters, not just limiting ourselves to selecting 4)
Please note: I do not use the Private Messaging system! I will not see any PMs that you send to me!!
Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me
