How many ways are there to arrange the letters in the word

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 17, 2019 5:01 am

BTGmoderatorDC wrote:How many ways are there to arrange the letters in the word Tennessee?

A. 1
B. 1260
C. 3780
D. 7560
E. 11340

OA C

Source: Veritas Prep

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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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In TENNESSEE :
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

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jun 19, 2019 5:36 pm

BTGmoderatorDC wrote:How many ways are there to arrange the letters in the word Tennessee?

A. 1
B. 1260
C. 3780
D. 7560
E. 11340

OA C

Source: Veritas Prep

If the letters in Tennessee were all different, then we could arrange the letters in 9! ways. However, there are 4 occurrences of the letter e and 2 occurrences each of the letters n and s. We use the indistinguishable permutations formula, which requires that we divide by the factorial of each of the number of indistinguishable letters. Thus, the number of ways one can arrange the letters in Tennessee is:

9!/(4!2!2!) = 3780

Answer: C

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