A certain car dealership offers its newest model in ten exterior and ten interior colors. If the eight interior colors are identical to the eight 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?  Pick:
A) 45
B) 72
C) 90
D) 10!/2!
E) 10!
I lined up the 9 different colours for Exterion and Interior like this:   E: A B C D E F G H I   I: A B C D E F G H I   I calculated the number of combinations:  9*9= 
<gadget id="calculator"> 9*9</gadget>
<output>81</output>
81 combinations.   But, from these 100 we need to delete sth: the same colours.   There are 9 possible pairs of coulours that will be the same. So, I deleted these 9 pairs from 81, resulting in 72.   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...).   72
<result>B</result>
A certain car dealership offers its newest model in ten exterior and ten interior colors. If the eight interior colors are identical to the eight 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?