lcpanam wrote:How many distinguishable permutations of letters are possible in the word Tennessee?

I understand this word has 9 letters, with 1-T, 4-E, 2-N, and 2-S. But, how do I solve this? I have tried finding step by step, many show answer of 3780, but how do I get to that answer? Also, what does it mean when there is an explanation point next to the number?

Thank you for helping me learn this. I am using a TI-83 calculator also.

When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]

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No onto your question.
The letters in TENNESSEE are follows:
There are 9 letters in total
There are 4 identical E's
There are 2 identical N's
There are 2 identical S's
So, the total number of possible arrangements = 9!/[(4!)(2!)(2!)]
= 3780

Cheers,
Brent

Hi icpanam,

Brent's correctly explained how that type of permutation math "works", so I won't rehash any of that here. Permutation questions aren't that common on Test Day (you'll likely see just 1-3), and since this question is a rare 'sub-category' of Permutations, you're not likely to see it on the actual GMAT at all. This is all meant to say that your missing points in the Quant section are likely from some other category (or categories).

As an aside, practicing with a calculator is NOT REALISTIC - you're not going to have access to one on Test Day, so you should not be using one now.

GMAT assassins aren't born, they're made,
Rich