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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: 53066
How many strings of 6 letters can be made using only the letters A, B,  [#permalink]

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16 Oct 2016, 05:55
00:00

Difficulty:

25% (medium)

Question Stats:

74% (00:59) correct 26% (01:54) wrong based on 111 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

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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, 06:05
1
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, 20:25
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, which contains A, B, and C:
For EACH pick, i.e., for ALL of the six slots, you have 3 choices, A, B, or C

Using "A" for the first pick does not make "A" unavailable for the next pick.

You could have AAAAAA, CCCBBB, or BCBCBCA, e.g. - 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, containing 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.
Add because this scenario is a true OR scenario. There is NO overlap between {A,B,C} ("only," per the prompt) and {D,E,F} "only"

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

OR, as I have seen happen
-- if you pay too much attention to the rule that "exponents do not distribute across addition!"

and hence do not notice that $$(n + n) = (2 * n)$$, then

-- Factor out $$3^6$$:
$$(3^6 + 3^6) = 3^6(1+1)=(3^6*2)$$
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How many strings of 6 letters can be made using only the letters A, B,   [#permalink] 15 Dec 2017, 20:25
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