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# In how many ways can 3 letters out of 5 distinct letters A

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Re: In how many ways can 3 letters out of 5 distinct letters A  [#permalink]

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01 Nov 2016, 21:08
Vishvesh88 wrote:
VeritasPrepKarishma : Yeah i got the mistake. But i'm looking at alternative methods to reach the answer.

Any other effective method? Kindly do share.

None better than: in-how-many-ways-can-3-letters-out-of-5-distinct-letters-a-123385.html#p1004825
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Re: In how many ways can 3 letters out of 5 distinct letters A  [#permalink]

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25 Feb 2017, 08:05
1) There are 5 letter that can be selected for the 1st place; 4 letters - for the 2nd place; and 3 letters for the 3rd place. Total: 5*4*3=60
2) There are 1*1*3=3 letter combinations that include both A and B
3) These 3 combinations can be arranged in 3! different ways 3*3!=18
4) Now you have to think about all the possible scenarios that include both A and B: AB*(3), *AB(3), BA*(3),*BA(3) scenarios have A and B together, but A*B and B*A scenarios do not.
5) We need to deduct the first category 3+3+3+3=12 out of the total number of arrangements: 60-12=48
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Re: In how many ways can 3 letters out of 5 distinct letters A  [#permalink]

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07 Jul 2018, 02:14
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: In how many ways can 3 letters out of 5 distinct letters A &nbs [#permalink] 07 Jul 2018, 02:14

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