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

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Bunuel
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How many different arrangements of letters are possible, if three lett [#permalink] New post   03 Apr 2017, 00:23
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68% (00:49) correct 32% (00:54) wrong based on 209 sessions
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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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B
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Re: How many different arrangements of letters are possible, if three lett [#permalink] 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
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matthewsmith_89
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Re: How many different arrangements of letters are possible, if three lett [#permalink] 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] 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] New post   06 Apr 2017, 09:33
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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


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] New post   10 Jul 2019, 07:32
oops. I got the answer as 5P3 and then calculated it wrongly :(
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ScottTargetTestPrep
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Re: How many different arrangements of letters are possible, if three lett [#permalink] New post   28 Jul 2019, 10:38
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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


The number of 3-letter arrangements is 5P3 = 5 x 4 x 3 = 60.

Alternate Solution:

There are 5 letters available for the first choice, and then 4 letters available for the second choice, and then 3 letters available for the third choice. Using the multiplication principle, we have 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]
28 Jul 2019, 10:38
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