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Re: In how many ways can the letters of the word OCARINA be arranged if th [#permalink]
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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!
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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= \(4C2*2 =12 \)

ANSWER B
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Re: In how many ways can the letters of the word OCARINA be arranged if th [#permalink]
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
Answer B
GMAT Club Bot
Re: In how many ways can the letters of the word OCARINA be arranged if th [#permalink]
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