GRE Prep 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.
In how many ways can the letters of the word GARGANTUNG be
[#permalink]
09 May 2019, 02:07
09 May 2019, 02:07
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
54% (01:14) correct
45% (01:12) wrong based on 46 sessions
Hide Show timer Statistics
In how many ways can the letters of the word GARGANTUNG be rearranged such that all the G’s appear together?
(A) \(\frac{8!}{3!*2!*2!}\)
(B) \(\frac{8!}{2!*2!}\)
(C) \(\frac{8!*3!}{2!*2!}\)
(D) \(\frac{8!}{2!*3!}\)
(E) \(\frac{10!}{3!*2!*2!}\)
(A) \(\frac{8!}{3!*2!*2!}\)
(B) \(\frac{8!}{2!*2!}\)
(C) \(\frac{8!*3!}{2!*2!}\)
(D) \(\frac{8!}{2!*3!}\)
(E) \(\frac{10!}{3!*2!*2!}\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In how many ways can the letters of the word GARGANTUNG be
[#permalink]
09 May 2019, 09:08
09 May 2019, 09:08
5
Carcass wrote:
In how many ways can the letters of the word GARGANTUNG be rearranged such that all the G’s appear together?
(A) \(\frac{8!}{3!*2!*2!}\)
(B) \(\frac{8!}{2!*2!}\)
(C) \(\frac{8!*3!}{2!*2!}\)
(D) \(\frac{8!}{2!*3!}\)
(E) \(\frac{10!}{3!*2!*2!}\)
(A) \(\frac{8!}{3!*2!*2!}\)
(B) \(\frac{8!}{2!*2!}\)
(C) \(\frac{8!*3!}{2!*2!}\)
(D) \(\frac{8!}{2!*3!}\)
(E) \(\frac{10!}{3!*2!*2!}\)
----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!)]
---------------------------
First, "GLUE" the 3 G's together to form ONE super letter (which we'll call X)
So, we must arrange the letters in the word: ARANTUNX
There are 8 letters in total
There are 2 identical A's
There are 2 identical N's
So, the total number of possible arrangements = 8!/[(2!)(2!)]
Answer: B
Cheers,
Brent
General Discussion
Re: In how many ways can the letters of the word GARGANTUNG be
[#permalink]
26 Nov 2019, 23:20
26 Nov 2019, 23:20
GreenlightTestPrep wrote:
Carcass wrote:
In how many ways can the letters of the word GARGANTUNG be rearranged such that all the G’s appear together?
(A) \(\frac{8!}{3!*2!*2!}\)
(B) \(\frac{8!}{2!*2!}\)
(C) \(\frac{8!*3!}{2!*2!}\)
(D) \(\frac{8!}{2!*3!}\)
(E) \(\frac{10!}{3!*2!*2!}\)
(A) \(\frac{8!}{3!*2!*2!}\)
(B) \(\frac{8!}{2!*2!}\)
(C) \(\frac{8!*3!}{2!*2!}\)
(D) \(\frac{8!}{2!*3!}\)
(E) \(\frac{10!}{3!*2!*2!}\)
----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!)]
---------------------------
First, "GLUE" the 3 G's together to form ONE super letter (which we'll call X)
So, we must arrange the letters in the word: ARANTUNX
There are 8 letters in total
There are 2 identical A's
There are 2 identical N's
So, the total number of possible arrangements = 8!/[(2!)(2!)]
Answer: B
Cheers,
Brent
What if the letter would be ACCLAIM ?
