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# How many different groups of three distinct letters are possible if th

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Math Expert
Joined: 02 Sep 2009
Posts: 56251
How many different groups of three distinct letters are possible if th  [#permalink]

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26 Apr 2017, 08:41
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Difficulty:

45% (medium)

Question Stats:

64% (01:23) correct 36% (01:43) wrong based on 149 sessions

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How many different groups of three distinct letters are possible if the three letters are chosen from the letters A, B, C, D, and E and A must be one of the letters selected?

A. 60
B. 10
C. 6
D. 4
E. 3

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Joined: 09 Jan 2016
Posts: 103
GPA: 3.4
WE: General Management (Human Resources)
Re: How many different groups of three distinct letters are possible if th  [#permalink]

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26 Apr 2017, 10:44
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[quote="Bunuel"]How many different groups of three distinct letters are possible if the three letters are chosen from the letters A, B, C, D, and E and A must be one of the letters selected?

A. 60
B. 10
C. 6
D. 4
E. 3[/quote
5c3= 10 we need to find out that A has to be included in the three group, and find how three group can be found out without the A.
4c3= 4 .
thus 10-4 equals 6.
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Re: How many different groups of three distinct letters are possible if th  [#permalink]

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02 Aug 2017, 03:22
Each group must have letter A and any two from the options BCDE.
Hence we should have 4C2 ways i.e. groups.
Option C.
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Joined: 15 Jan 2018
Posts: 7
Re: How many different groups of three distinct letters are possible if th  [#permalink]

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16 Mar 2018, 03:52
Thanks in advance for any response!!!

why is the below method not correct?
A _ _ , A has to be one of the letters. For the remaining 2 position it will be --> 4c1*3c1=12.

Since, the correct answer is 6, the possible groups are:
ABC, ABD, ABE, ACD, ACE, ADE.
Each group can again be arranged in 3! ways. So, What would the approach/solution be if the question asked for number of arrangements?
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Joined: 26 Feb 2016
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Location: India
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How many different groups of three distinct letters are possible if th  [#permalink]

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16 Mar 2018, 07:01
1
Thanks in advance for any response!!!

why is the below method not correct?
A _ _ , A has to be one of the letters. For the remaining 2 position it will be --> 4c1*3c1=12.

Since, the correct answer is 6, the possible groups are:
ABC, ABD, ABE, ACD, ACE, ADE.
Each group can again be arranged in 3! ways. So, What would the approach/solution be if the question asked for number of arrangements?

Here for the question being asked, in the 12 options possible when
you use 4c1*3c1 - AED and ADE are both possible(but since we are
asked to find the total possible groups) it would be wrong!

"total number of arrangements possible if A is one of the letters "
One of the letters will be A.
The other two letter can be chosen as 4c2 = 6
There are 3!(6) ways of arranging them.

Total arrangments possible are 1*6*6 = 36

Hope this helps you!
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Re: How many different groups of three distinct letters are possible if th  [#permalink]

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19 Mar 2018, 16:11
Bunuel wrote:
How many different groups of three distinct letters are possible if the three letters are chosen from the letters A, B, C, D, and E and A must be one of the letters selected?

A. 60
B. 10
C. 6
D. 4
E. 3

First, we know this will be a combination problem, since the order of selection doesn’t matter.

Since A must be selected, we are actually choosing only 2 letters from the 4 letters: B,C,D,E. Thus, the selection can be made in 4C2 = (4 x 3)/2 = 6 ways.

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Re: How many different groups of three distinct letters are possible if th   [#permalink] 19 Mar 2018, 16:11
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