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Find the number of selections that can be made taking 4 lett

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Find the number of selections that can be made taking 4 lett  [#permalink]

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New post 29 Jul 2010, 20:09
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Difficulty:

  95% (hard)

Question Stats:

37% (01:12) correct 63% (01:41) wrong based on 150 sessions

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Find the number of selections that can be made taking 4 letters from the word "ENTRANCE".

(A) 70
(B) 36
(C) 35
(D) 72
(E) 32
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Posts: 47112
Re: Triangles and letters!  [#permalink]

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New post 29 Jul 2010, 20:24
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dungtd wrote:
Find the number of selections that can be made taking 4 letters from the word "ENTRANCE".
(A) 70
(B) 36
(C) 35
(D) 72
(E) 32

Thanks for your kind help!


This problem is not the one you'll see on real GMAT. As combinatorics problems on GMAT are quite straightforward. But still it could be good for practice.

We have 8 letters from which 6 are unique.

Possible scenarios for 4 letter selection are:
A. All letters are different;
B. 2 N-s and other letters are different;
C. 2 E-s and other letters are different;
D. 2 N-s, 2 E-s.

Let's count them separately:
A. All letters are different, means that basically we are choosing 4 letters form 6 distinct letters: 6C4=15;
B. 2 N-s and other letters are different: 2C2(2 N-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;
C. 2 E-s and other letters are different: 2C2(2 E-s out of 2)*5C2(other 2 letters from distinct 5 letters left)=10;;
D. 2 N-s, 2 E-s: 2C2*2C2=1.

15+10+10+1=36

Answer: B.
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Re: Find the number of selections that can be made taking 4 lett  [#permalink]

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New post 08 Sep 2014, 22:58
dungtd wrote:
Find the number of selections that can be made taking 4 letters from the word "ENTRANCE".

(A) 70
(B) 36
(C) 35
(D) 72
(E) 32



Yes, there is no zing in the question. It involves laborious counting of cases and hence isn't a GMAT type of question.
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Re: Find the number of selections that can be made taking 4 lett  [#permalink]

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New post 12 Nov 2017, 08:12
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: Find the number of selections that can be made taking 4 lett &nbs [#permalink] 12 Nov 2017, 08:12
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