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# How many strings of 6 letters can be made using only the letters A, B,

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Math Expert
Joined: 02 Sep 2009
Posts: 44573
How many strings of 6 letters can be made using only the letters A, B, [#permalink]

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16 Oct 2016, 06:55
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74% (00:50) correct 26% (01:14) wrong based on 91 sessions

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How many strings of 6 letters can be made using only the letters A, B, and C, or only the letters D, E, and F ?

A. 2×3^6
B. 3×2^6
C. 3×3^6
D. 2×2^6
E. 6^6
[Reveal] Spoiler: OA

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Joined: 18 Jun 2016
Posts: 98
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 700 Q49 V36
Re: How many strings of 6 letters can be made using only the letters A, B, [#permalink]

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16 Oct 2016, 07:05
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KUDOS
Bunuel wrote:
How many strings of 6 letters can be made using only the letters A, B, and C, or only the letters D, E, and F ?

A. 2×3^6
B. 3×2^6
C. 3×3^6
D. 2×2^6
E. 6^6

3^6 + 3^6 = 2*3^6

IMO : A
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How many strings of 6 letters can be made using only the letters A, B, [#permalink]

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15 Dec 2017, 21:25
Bunuel wrote:
How many strings of 6 letters can be made using only the letters A, B, and C, or only the letters D, E, and F ?

A. 2×3^6
B. 3×2^6
C. 3×3^6
D. 2×2^6
E. 6^6

Using FCP or "slot" method.
There are six slots.
The total possibilities are calculated by:
# of possibilities for 1st pick *
# of possibilities for 2nd pick *
# of possibilities for 3rd pick, etc.

For Set 1, with A, B, and C:
For each pick, for ALL of the six slots, you have 3 choices, A, B, or C

You could have AAAAAA, e.g. or BCBCBCA - order doesn't matter, repetition is allowed.

3 x 3 x 3 x 3 x 3 x 3 =$$3^6$$ for Set 1

Set 2, with just letters D, E, and F, gets calculated exactly the same way as Set 1.
So Set 2's total possibilities = $$3^6$$

Then you add the separate cases' possibilities.

$$(3^6 + 3^6) = (2 * 3^6)$$

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How many strings of 6 letters can be made using only the letters A, B,   [#permalink] 15 Dec 2017, 21:25
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