A certain car dealership offers its newest model in ten exterior and ten interior colors. If the seven interior colors are identical to the seven 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:
A) 45	B) 81	C) 90	D) 10!/2!	E) 10!
I lined up the 10 different colours for Exterion and Interior like this:   E: A B C D E F G H I J   I: A B C D E F G H I J   I calculated the number of combinations:   10*10= 
<gadget id="calculator">  10*10</gadget>
<output>100</output>
100 combinations.   But, from these 100 we need to delete sth: the same colours.   There are 10 possible pairs of coulours that will be the same. So, I deleted these 10 pairs from 100, resulting in 45.   Mind here, that the 10 do not result in 20 colours, because 1 pair is one unit that is not allowed. So, 10 units are not allowed (surprised that 80 wasn't among the answer options to confuse test takers...).   45
<result>A</result>
A certain car dealership offers its newest model in ten exterior and ten interior colors. If the seven interior colors are identical to the seven 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?