You are assigned to design color codes for different parts. Three colors are used to code on each part. Once a combination of three colors is used-such as green,yellow,and red-these three colors cannot be rearranged to use as a code for another part. If there are 35 combinations,how many colors are available?
A)5
B)7
C)9
D)11

Question

Quizplus · Accepted Answer

Since there are 35 combinations and each combination requires three distinct colors, the total number of available colors can be calculated as 35 divided by the number of unique combinations that can be formed with three colors. This number is equal to 35 divided by the total number of combinations of 3 colors chosen from the total number of colors available. Using the formula for combinations (n choose r) = n!/r!(n-r)!, we can calculate that the total number of color choices must be a whole number greater than or equal to 7 and less than 8 (i.e., 35 / (n choose 3) = a whole number). The only whole number in this range that satisfies this condition is 7, so the answer is B, 7.

You Are Assigned to Design Color Codes for Different Parts