You have the assignment of designing colour codes for different parts. Three colours are to be used on each part, but a combination of three colours 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 colours) could not be used to identify a pinion gear. If there are 35 combinations, how many colours were available?
A) 5
B) 7
C) 9
D) 11
E) None of the choices are correct

Question

Quizplus · Accepted Answer

The number of combinations of 3 colors from n available colors is given by the combination formula C(n, 3) = n! / (3!(n-3)!). Setting this equal to 35, we solve for n: C(n, 3) = 35 => n(n-1)(n-2)/6 = 35. Solving this equation gives n = 7.

You Have the Assignment of Designing Colour Codes for Different