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

Question

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

Kudos for a correct  solution .

gmat6nplus1 · Answer

the answer should be C. 9!/4!(4)

shelrod007 · Answer

Answer is C .

In the word TENNESSEE .

For 9 letters , 2 N's are alike , 2 S's are alike and 4 E's are alike

Which results in

9! / ( 2!*2! * 4 ! ) = 9* 2* 7*6*5 = 3780 .

LaxAvenger · Answer

9 total words, 4 "E" , 2 "N" , 2 "S"

= 9! / 4! 2! 2! = 3780. Answer C

kdatt1991 · Answer

I used the standard textbook method: The basic formula to find out the number of total arrangements is x! , therefore Tenessee could be arranged in 9! ways. But the word 'Tennessee' consists of 2 letters of 'n's, 2 letters of 's's and 4 letters of e's. So, we need to divide the total number of arrangements by 2! (to account for the 'n's) 2! (to account for the 's's) and 4! (to account for the 'e's). Therefore \frac{9!}{2!2!4!} = \frac{9*8*7*6*5}{4} = 9*7*6*5*2 = 3780 . Out of curiosity, is there any other way we could solve this problem?...please let me know. Please consider giving me KUDOS if you felt this post was helpful! Thanks.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: (C)

Remember your formula for Permutations with Repeating Elements: N!/A!B!..., such that N is the total number of letters to be arranged and A, B, and any other values in the denominator are the number of each repeating element that you have. In our case the formula could be expressed as 9!/2!4!2!, where 9 is the total number of letters, 2 the number of N’s, 4 the number of E’s, and the other 2 the number of S’s. From here, simplify. The fraction can be rewritten as (9 * 8 * 7 * 6 * 5) / 2 * 2, or (9 * 7 *6 * 5 * 2). From here, multiply quickly: 9 * 42 * 10 = 9 * 420 = about 3600, or answer (C).

ScottTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards