A certain car dealership offers its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?
Choose the correct choice from the following answers.
A) 45	B) 81	C) 90	D) 10!/2!	E) 10!
The question says there are 10 different colors.   Since interior and exterior are to be painted with different colors, the order is important while counting the color combination.   Therefore, the number of possible ways can be found out by permutation of 2 colors out of 10 colors.   10P2 = 10!/(10-2)! = 10!/8! = 90 [10P2 = 10902*2!]   Answer: (90
<result>C</result>
A certain car dealership offers its newest model in ten exterior and ten interior colors. If the ten interior colors are identical to the ten exterior colors, and the dealership sells every pair of colors except those that would result in a car with an identically colored interior and exterior, how many different color combinations are possible?