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

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

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New post 08 Apr 2016, 02:45
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

51% (00:45) correct 49% (00:31) wrong based on 149 sessions

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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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New post 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
Answer B
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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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New post 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
Answer B


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

Thanks
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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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New post 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!
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Re: In how many ways can the letters of the word OCARINA be arranged if th &nbs [#permalink] 20 Jan 2018, 21:12
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