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How many different arrangements of letters are possible, if three lett

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How many different arrangements of letters are possible, if three lett [#permalink]

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New post 03 Apr 2017, 00:23
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How many different arrangements of letters are possible, if three letters are chosen without replacement from the letters A, B, C, D, and E to make the arrangement?

A. 120
B. 60
C. 20
D. 10
E. 6

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Re: How many different arrangements of letters are possible, if three lett [#permalink]

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New post 03 Apr 2017, 03:18
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Bunuel wrote:
How many different arrangements of letters are possible, if three letters are chosen without replacement from the letters A, B, C, D, and E to make the arrangement?

A. 120
B. 60
C. 20
D. 10
E. 6


three letters are chosen without replacement from the letters A, B, C, D, and E in 5C3 ways = 10
these 3 letter thus selected can be arranged in 3P3 ways = 3! = 6
different arrangements of letters possible = 6*10 = 60

IMO option B is correct
Hit Kudos if you liked it 8-)
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Re: How many different arrangements of letters are possible, if three lett [#permalink]

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New post 03 Apr 2017, 12:16
Another approach:

5P3 = 5!(5-3!) = 60

Answer B
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Re: How many different arrangements of letters are possible, if three lett [#permalink]

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New post 03 Apr 2017, 23:35
Why can't we just use 5!/3! here? Or 5C3?
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Re: How many different arrangements of letters are possible, if three lett [#permalink]

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New post 06 Apr 2017, 09:33
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Expert's post
Bunuel wrote:
How many different arrangements of letters are possible, if three letters are chosen without replacement from the letters A, B, C, D, and E to make the arrangement?

A. 120
B. 60
C. 20
D. 10
E. 6


We are given that there are 5 letters and we need to arrange 3 of them. Since we have an “order arrangement,” order matters. So we have a permutation problem. Thus, the number of ways to arrange 3 letters from 5 is:

5P3 = 5!/(5-3)! = 5 x 4 x 3 = 60

Answer: B
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Re: How many different arrangements of letters are possible, if three lett [#permalink]

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New post 11 Apr 2018, 16:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many different arrangements of letters are possible, if three lett   [#permalink] 11 Apr 2018, 16:50
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