GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 00:59

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In how many ways can the letters of the word OCARINA be arranged if th

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58427
In how many ways can the letters of the word OCARINA be arranged if th  [#permalink]

### Show Tags

08 Apr 2016, 02:45
00:00

Difficulty:

35% (medium)

Question Stats:

60% (01:00) correct 40% (00:52) wrong based on 164 sessions

### HideShow timer Statistics

In how many ways can the letters of the word OCARINA be arranged if the O, R, and N remain in their original positions?

A. 6
B. 12
C. 18
D. 24
E. 48

_________________
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2400
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: In how many ways can the letters of the word OCARINA be arranged if th  [#permalink]

### Show Tags

08 Apr 2016, 21:27
The word OCARINA has 7 letters and if the O, R, and N remain in their original positions
then we have 4 positions to arrange the remaining letters - C , 2A , I

Number of ways = 4!/2!
= 12
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Intern
Joined: 15 Jan 2016
Posts: 36
Re: In how many ways can the letters of the word OCARINA be arranged if th  [#permalink]

### Show Tags

20 Jan 2018, 11:04
Skywalker18 wrote:
The word OCARINA has 7 letters and if the O, R, and N remain in their original positions
then we have 4 positions to arrange the remaining letters - C , 2A , I

Number of ways = 4!/2!
= 12

I'm confused. Can you please explain why you divided by 2!? From my understanding order matters here.

Thanks
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: In how many ways can the letters of the word OCARINA be arranged if th  [#permalink]

### Show Tags

20 Jan 2018, 21:12
syedazeem3 wrote:

I'm confused. Can you please explain why you divided by 2!? From my understanding order matters here.

Thanks

We have 2 A's in OCARINA. Since you cannot differentiate between the 2 identical A's the permutations between these 2 A's don't matter and hence you remove those possibilities by dividing with 2!
Re: In how many ways can the letters of the word OCARINA be arranged if th   [#permalink] 20 Jan 2018, 21:12
Display posts from previous: Sort by