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

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Math Expert
Joined: 02 Sep 2009
Posts: 52271
How many different arrangements of letters are possible, if three lett  [#permalink]

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02 Apr 2017, 23:23
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:49) correct 30% (00:46) wrong based on 113 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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Re: How many different arrangements of letters are possible, if three lett  [#permalink]

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03 Apr 2017, 02:18
1
1
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
Manager
Joined: 06 Dec 2016
Posts: 248
Re: How many different arrangements of letters are possible, if three lett  [#permalink]

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03 Apr 2017, 11:16
Another approach:

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

Intern
Joined: 09 Jan 2017
Posts: 6
Re: How many different arrangements of letters are possible, if three lett  [#permalink]

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03 Apr 2017, 22:35
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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06 Apr 2017, 08:33
1
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

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

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11 Apr 2018, 15:50
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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 &nbs [#permalink] 11 Apr 2018, 15:50
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