Question

You have the assignment of designing 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 were available?

Answer 1

The formula for the number of combinations of choosing "r" objects from a larger set of "n" is
combinations = n! / r! * (n - r)!
we know combinations = 35 and r = 3 so we have to solve for "n"
35 = n! / 3! * (n -3)!
n = 7 colors were available