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

Question

Quizplus · Accepted Answer

Since each part can be identified using a unique combination of 3 colours, we can treat each combination as a distinct element. There are 35 such elements, which is equivalent to the number of ways of choosing 3 elements out of n. This can be expressed as nC3 = 35, which gives n(n-1)(n-2)/6 = 35. Solving for n, we get n = 7. Therefore, there were 7 colours available.

You Have the Assignment of Designing Colour Codes for Different