In how many ways can the letters of the word "Establish" be rearranged

Question

In how many ways can the letters of the word "Establish" be rearranged such that the vowels always appear together?

A. 5,040
B. 15,120
C. 30,240
D. 40,320
E. 241,920

Arpitkumar2310 · Answer

Considering eai as one letter, the total number of letters are 7. It can arranged in 7!/2! ways. Eai can be arranged in 3! ways. Total number of ways 7!/2! x 3! = 2520 x 6 = 15120.

Posted from my mobile device

Lampard42 · Answer

The vowels can be arranged among themselves in 3! ways.
The other letters + 1 (consider vowels as 1 set) in 7! Ways.
Total possible arrangement is 7!*3! = 30240 Option C

firas92 · Answer

Consider the vowels EAI as one letter so now we have (EAI)STBLSH

This can be arranged in 7!/2! ways (since S is repeated) and the vowels themselves can be arranged in 3! ways

Final answer is 7!*3!/2! = 15120

Answer is  (B)

Hit Kudos if this helped!

Posted from my mobile device

Archit3110 · Answer

ESTABLISH
V= EAI ; 3!
C=STBLSH ; 
VSTBLSH = arranged in 7!/2! and 3! for C
TOTAL WAYS VSTABLSH ; 3!*7!/2! ; 15120
IMO B

GmatPrime · Answer

Bunuel

Establish has 2 's' alphabets. So shouldn't we divide 7! by 2! ?

7!/ 2! * (3!) = 15,120 (option B)

firas92 · Answer

Hi  Bunuel

I have the same query as quoted. Please provide an explanation

Posted from my mobile device

Bunuel · Answer

There are 9 letters, out of which three, E, A, and I, are vowels.

Consider then as one unit {EAI}, so we get 7 items: {S}{S}{T}{B}{L}{H}{EAI}. Those, 7 can be arranged in 7!/2 ways. E, A, and I, within their unit can be arranged in 3! ways, so the total number of arrangements when vowels are together is 7!/2*3! = 15,120.

Answer: B.

ScottTargetTestPrep · Answer

We treat the 3 vowels as a single item, as shown here:

- S-T-B-L-S-H

In essence, we are arranging only 7 items.The number of ways to arrange   - S-T-B-L-S-H is 7!. We must also consider that the 3 vowels can also be rearranged, and the number of ways to arrange   is 3! Additionally, since we have two S’s (indistinguishable), we must divide by 2!; thus, we have:

(7! x 3!)/2! = 7! x 3 = 5,040 x 3 = 15,120

Answer: B

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.

In how many ways can the letters of the word "Establish" be rearranged

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

In how many ways can the letters of the word "Establish" be rearranged

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