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!

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 )

Please recheck the OA.

Answer should be

B
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Kindly press Kudos if the explanation is clear.

Thank you

Ambarish