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 seven colors?
Select
A) 21  B) 35  C) 105  D) 135  E) 210
Combinations = N!/[K!(N-K)!] where N is the total number of items and K is the size of the subgroup   Here, we have 7 colors and we're choosing combinations of 3. Plugging those values in, we get...   7!/(3!4!) = (7)(6)(5)/(3)(2)(1) = (7)(5) = 35 combinations of 3 colors.   Final Answer:35
<result>B</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 seven colors?