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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Jun 16, 2019 9:55 pm

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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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Source: Beat The GMAT — Problem Solving | Sun Jun 16, 2019 9:55 pm

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

------------ASIDE-----------------
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!)]
---------------------------------------

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: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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