Question

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 in green, yellow and violet were used to identify a cam shaft, yellow, violet and green (or and combination of these three colors) could not be used to identify a pinion gear. If there are 35 combinations, how many colors are available

Answer 1

Answer:

7 available

Explanation:

Since 3 colors are available r = 3

Total combination = 35

nCr = 35 ---1

nCr = n!/(n-r)!r!---2

We put equation 1 and 2 together

n-1)(n-2)(n-3)!/n-3)! = 35x 3!

We cancel out (n-3)!

(n-1)(n-2) = 210

7x6x5 = 210

nC3 = 35

7C3 = 35

So If there are 35 combinations, 7 colors are available.

Thank you!