You have the assignment of designing color codes for different parts. Three colors are used on each part, but a combination of three colors used for one part cannot be rearranged and used to identify a different part. This means that if green, yellow and violet were used to identify a camshaft, yellow, violet and green (or any other combination of these three colors) could not be used to identify a pinion gear. If there are 35 combinations, how many colors were available?
A) 5
B) 7
C) 9
D) 11

Question

Quizplus · Accepted Answer

If we assume that each color can be used in combination with the others, we have 3 choices for the first color, 2 choices for the second color (since one color has already been chosen), and only 1 choice for the third color (since two colors have already been chosen). This gives us 3x2x1=6 possible combinations for each part. However, we are given that each combination can only be used once, which means that we can have a maximum of 35 combinations if we have 7 available colors (35=7x5). Therefore, the answer is 7.

You Have the Assignment of Designing Color Codes for Different