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# A Car comes with 7 different possible exterior colors and 6

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A Car comes with 7 different possible exterior colors and 6 [#permalink]  10 Feb 2011, 11:49
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A Car comes with 7 different possible exterior colors and 6 different interior colors. How many different color combinations are there?

$$A. 26$$

$$B. 42$$

$$C. \frac{7!6!}{2!}$$

$$D. 7!6!$$

$$E. \frac{13!}{2!}$$
[Reveal] Spoiler: OA

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Re: Color Combinations [#permalink]  10 Feb 2011, 11:56
Expert's post
gmatpapa wrote:
A Car comes with 7 different possible exterior colors and 6 different interior colors. How many different color combinations are there?

$$A. 26$$

$$B. 42$$

$$C. \frac{7!6!}{2!}$$

$$D. 7!6!$$

$$E. \frac{13!}{2!}$$

Why not
[Reveal] Spoiler:
D

For each exterior color out of 7 there are 6 different interior colors possible, so there are total of 7*6=42 color combinations. This is basically the same as Principle of Multiplication: if one event can occur in $$m$$ ways and a second can occur independently of the first in $$n$$ ways, then the two events can occur in $$mn$$ ways.

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Re: Color Combinations [#permalink]  10 Feb 2011, 12:36
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$$C^7_1*C^6_1$$
$$7*6=42$$

Ans: "B"
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Re: Color Combinations [#permalink]  10 Feb 2011, 15:53
42
This one was suspiciously easy - I spent one minute only thinking about the trap - little bit paranoid.
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Re: A Car comes with 7 different possible exterior colors and 6 [#permalink]  21 Oct 2014, 14:01
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Re: A Car comes with 7 different possible exterior colors and 6 [#permalink]  21 Oct 2014, 14:27
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craky wrote:
42
This one was suspiciously easy - I spent one minute only thinking about the trap - little bit paranoid.

I think that is a common problem. I know I've actually spent too long on a problem because I didn't trust in myself that I could have gotten a problem so easily. One way to get around this is to practice a lot so that you gain more confidence in your abilities and realize that the test will give you very easy questions sometimes.
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Veritas Prep Statistics and Combinatorics Homework Question#74 [#permalink]  24 May 2015, 20:58
A car is available in seven different exterior colors and six different interior colors. how many unique color combinations are possible?

(A) 26
(B) 42
(C) 7!6!/2!
(D) 7!6!
(E) 13!/2!

[Reveal] Spoiler:
OA : (C)

Why the OA is correct, what am I missing? My answer choice is (D)
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Re: Veritas Prep Statistics and Combinatorics Homework Question#74 [#permalink]  24 May 2015, 22:39
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sandeepmanocha wrote:
A car is available in seven different exterior colors and six different interior colors. how many unique color combinations are possible?

(A) 26
(B) 42
(C) 7!6!/2!
(D) 7!6!
(E) 13!/2!

[Reveal] Spoiler:
OA : (C)

Why the OA is correct, what am I missing? My answer choice is (D)

There are 7 different ways to choose an exterior color and 6 different ways to choose an interior color.
So the number of combinations is 7 * 6 = 42.

(Imagine A B C D E F G are the choices for exterior colors and H I J K L M are the choices for interior colors.
If you choose A as the exterior color you can choose any of H I J K L M as interior color. So 6 combinations when you choose A as exterior.
Similarly
If you choose B as the exterior color you can choose any of H I J K L M as interior color. So 6 combinations when you choose B as exterior.
So you can see that for each exterior color there is an option of 6 interior colors. So total possible combinations = 7*6 = 42 )

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Veritas Prep Statistics and Combinatorics Homework Question#74 [#permalink]  24 May 2015, 22:57

Yes, you are right, I looked at wrong answer choice
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Re: A Car comes with 7 different possible exterior colors and 6 [#permalink]  25 May 2015, 00:41
Expert's post
sandeepmanocha wrote:
A car is available in seven different exterior colors and six different interior colors. how many unique color combinations are possible?

(A) 26
(B) 42
(C) 7!6!/2!
(D) 7!6!
(E) 13!/2!

[Reveal] Spoiler:
OA : (C)

Why the OA is correct, what am I missing? My answer choice is (D)

Merging topics.

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Re: A Car comes with 7 different possible exterior colors and 6   [#permalink] 25 May 2015, 00:41
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