At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using six colors? Choose the correct choice from the following options
A) 20  B) 35  C) 105  D) 135  E) 210
The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.   20s an example, a chemical with the colors 20/B/C means that the following combinations C20NNOT be used by any other chemical:   20BC   20CB   B20C   BC20   C20B   CB20   By extension, the first part of your calculation would be the number of possible substances that could be identified with 6 colors: 6c3 = 20 possible substances   20
<result>A</result>
At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using six colors?