Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 2708:30 AM PDT
-09:30 AM PDT
Next - GMAT Ninja CR series, we tackle a very specific flavor of Critical Reasoning: Plans & Goals questions. The GMAT loves to present a scenario where a company, government, or individual proposes a seemingly brilliant plan to achieve a specific goal.
May 2110:00 AM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.- May 28
08:30 AM PDT
-09:30 AM PDT
Are you constantly rereading GMAT RC passages but still struggling to understand them? Most students think rereading improves accuracy — but in reality, it usually signals a flawed reading strategy. - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
24 Nov 2021, 08:07
Kudos
Bookmarks
In how many ways can the letters of the word PERMUTATIONS be arranged such that the order of vowels remains unchanged?
A. \(\frac{12!}{2!}\)
B. \(\frac{12!}{5!}\)
C. \(\frac{12!}{2!*5!}\)
D. \(\frac{4*7!}{2!}\)
E. \(\frac{4*7!}{2!*5!}\)
A. \(\frac{12!}{2!}\)
B. \(\frac{12!}{5!}\)
C. \(\frac{12!}{2!*5!}\)
D. \(\frac{4*7!}{2!}\)
E. \(\frac{4*7!}{2!*5!}\)
17 Feb 2025, 22:26
Kudos
Bookmarks
Another way to think could be,
Total possible arrangements = 12!/2! (T is repeated twice)
Now notice that there are 5 different vowels and we want only one order out of the default 5! orders, so we will need to remove rest of the orders but one, which is nothing but,
12!/2! * 1/5! = 12!/(2!*5!)
It's like saying for ABC, out of all the orders possible, I just need ABC ie. 1 out of 3!
Ans: C
Total possible arrangements = 12!/2! (T is repeated twice)
Now notice that there are 5 different vowels and we want only one order out of the default 5! orders, so we will need to remove rest of the orders but one, which is nothing but,
12!/2! * 1/5! = 12!/(2!*5!)
It's like saying for ABC, out of all the orders possible, I just need ABC ie. 1 out of 3!
Ans: C
General Discussion
24 Nov 2021, 08:07
Kudos
Bookmarks
Official Solution:
In how many ways can the letters of the word PERMUTATIONS be arranged such that the order of vowels remains unchanged?
A. \(\frac{12!}{2!}\)
B. \(\frac{12!}{5!}\)
C. \(\frac{12!}{2!*5!}\)
D. \(\frac{4*7!}{2!}\)
E. \(\frac{4*7!}{2!*5!}\)
PERMUTATIONS has 12 letters: 5 vowels (EUAIO) and 7 consonants (PRMTTNS).
Choose 5 slots from 12 for the vowels: \(C^5_{12}=\frac{12!}{5!*7!}\). Since the order of the vowels must remain unchanged (EUAIO), then we do not arrange them.
7 consonants in 7 remaining slots can be arranged in \(\frac{7!}{2!}\) ways (notice that we have two T's among 7 consonants).
So, the total number of ways is \(\frac{12!}{5!*7!}*\frac{7!}{2!}=\frac{12!}{2!*5!}\).
Answer: C
In how many ways can the letters of the word PERMUTATIONS be arranged such that the order of vowels remains unchanged?
A. \(\frac{12!}{2!}\)
B. \(\frac{12!}{5!}\)
C. \(\frac{12!}{2!*5!}\)
D. \(\frac{4*7!}{2!}\)
E. \(\frac{4*7!}{2!*5!}\)
PERMUTATIONS has 12 letters: 5 vowels (EUAIO) and 7 consonants (PRMTTNS).
Choose 5 slots from 12 for the vowels: \(C^5_{12}=\frac{12!}{5!*7!}\). Since the order of the vowels must remain unchanged (EUAIO), then we do not arrange them.
7 consonants in 7 remaining slots can be arranged in \(\frac{7!}{2!}\) ways (notice that we have two T's among 7 consonants).
So, the total number of ways is \(\frac{12!}{5!*7!}*\frac{7!}{2!}=\frac{12!}{2!*5!}\).
Answer: C
