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# How many combinations of three letters taken from letters

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Joined: 02 May 2015
Posts: 193
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How many combinations of three letters taken from letters  [#permalink]

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15 Jul 2016, 05:29
Anjalika123 wrote:
Bunuel wrote:
bmwhype2 wrote:
How many combinations of three letters taken from letters (a, a, b, b, c, c, d) are possible?

A. 12
B. 13
C. 35
D. 36
E. 56

This kind of question has little chances appearing on the actual test.

Anyway, we have 7 letters {a, a, b, b, c, c, d}. There are 2 ways to select 3 letters out of this set:

CASE #1: all letters are distinct:

Since there are 4 distinct letters a, b, c and d, then the # of ways to select 3 out of 4 is 4C3=4.

CASE #2: 2 letters are the same and the third is different:

There are 3 letters from the set which can provide us with two letters: a, b, and c. 3C1=3 gives the # of ways to select which letter out of these 3 will provide us with 2 letters. For, example double letters can be aa, bb, or cc.

Next, we are left with 3 letters to choose the third letter. For example, if we choose aa, then b, c, and d are left to choose from for the third letter, thus the # of ways to do that is 3C1=3.

Total # of ways for this case is therefore 3C1*3C1=9.

Total for both cases = 4+9 = 13.

Hope it's clear.

Hi Bunnel ,
Let -->s (same letter)
--> d(distinct letter)
Then
In case 2(two same other distinct) shouldn't we consider these cases?
-->ssd >>3*3=9
-->sds >>3*3=9
--> dss >>3*3=9
so # of possibilities for case two =9*3=27

By your logic, you will be counting both aba and aab. Which is wrong. Also you haven't included ddd.
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Re: How many combinations of three letters taken from letters  [#permalink]

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21 Mar 2017, 00:43
Very good question !!!!!!
Looks simple at a glance, but required great use of logic.
Like this one.
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Re: How many combinations of three letters taken from letters  [#permalink]

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17 Apr 2018, 10:42
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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 combinations of three letters taken from letters &nbs [#permalink] 17 Apr 2018, 10:42

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