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## Need help to understand this combination & permutation p

This topic has 1 expert reply and 3 member replies
ktr32 Newbie | Next Rank: 10 Posts
Joined
12 Feb 2007
Posted:
7 messages

#### Need help to understand this combination & permutation p

Fri Feb 16, 2007 6:05 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
I have no clue where to begin to solve the problem, every approach I use, it seems to be wrong. I think my initial assumptions are wrong on how i am setting up the problem. Thanks

Problem 1.77 from Schaum's Outlines (Probability and Statistics 2nd Edition)

Problem:
Find the number (a) combinations and (b) permutations of 4 letters each that can be made from the letters of the word Tennessee.

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ktr32 Newbie | Next Rank: 10 Posts
Joined
12 Feb 2007
Posted:
7 messages
Fri Feb 16, 2007 2:02 pm
Okay, I figured out why the number of combinations are 17, but I had to write them all out I have listed them all below

4 - Unique letters (TSNE), 4 - E's, 2 - S's, 2 - N's, 1 - T

Total Combinations = UNIQUE + 4 E's + 3 E's + 2 E's + 2 S's + 2 N's

Combination list:
TSNE EEEE EEET EEES
EEEN EETN EETS EESS
EENN EESN SSTN SSEN
SSNN SSET NNTE NNTS
NNES

The big question how do you calculate the number of combinations with out having to write them out.

ktr32 Newbie | Next Rank: 10 Posts
Joined
12 Feb 2007
Posted:
7 messages
Fri Feb 16, 2007 2:50 pm
I figured out how entails some polynomial multiplication, i will post an answer to it later this evening.

ktr

### GMAT/MBA Expert

Stacey Koprince GMAT Instructor
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Mon Feb 19, 2007 11:40 pm
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)

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ktr32 Newbie | Next Rank: 10 Posts
Joined
12 Feb 2007
Posted:
7 messages
Tue Feb 20, 2007 8:01 am
Thanks for the response.

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