Last visit was: 20 Jul 2024, 08:35 It is currently 20 Jul 2024, 08:35
Toolkit
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
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 OCARINA be arranged if th

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94430
Own Kudos [?]: 642506 [4]
Given Kudos: 86706
Retired Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2093
Own Kudos [?]: 8987 [2]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Intern
Joined: 15 Jan 2016
Posts: 28
Own Kudos [?]: 21 [0]
Given Kudos: 487
Current Student
Joined: 13 Apr 2015
Posts: 1426
Own Kudos [?]: 4602 [1]
Given Kudos: 1228
Location: India
Re: In how many ways can the letters of the word OCARINA be arranged if th [#permalink]
1
Kudos
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!
Manager
Joined: 06 Oct 2019
Status:BELIEVE IN YOURSELF
Posts: 100
Own Kudos [?]: 177 [0]
Given Kudos: 90
Location: India
Re: In how many ways can the letters of the word OCARINA be arranged if th [#permalink]
Bunuel wrote:
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

O__ __ R __ N __

you have to 1st calculate the possible position of 2 A's

The no. of ways to place 2 A's= $$4C2=6$$ ways

1. OAAR__N__ = 2 ways (as C And I can arrange themselves in 2 ways)
2. O__ __ RANA =2 ways (as C And I can arrange themselves in 2 ways)
3. OA__ RAN__ =2 ways (as C And I can arrange themselves in 2 ways)
4. OA__ R__NA =2 ways (as C And I can arrange themselves in 2 ways)
5. O__ARAN__ = 2 ways (as C And I can arrange themselves in 2 ways)
6. O__AR__ NA =2 ways (as C And I can arrange themselves in 2 ways)

you don't have to write all those possibilities

Answer= $$4C2*2 =12$$

Manager
Joined: 09 Aug 2022
Posts: 85
Own Kudos [?]: 23 [0]
Given Kudos: 48
Location: India