Final answer:
There are 20 different ways to select three colors from six available colors for a printing job using combinations in mathematics. The combination formula C(n, r) is used because the order of selection does not matter, resulting in C(6, 3) = 6! / [3! * (6 - 3)!] = 20.
Step-by-step explanation:
To determine the number of ways we can select three colors for a printing job out of six available colors, we can use the concept of combinations from mathematics. The reason combinations are used instead of permutations is because the order in which the colors are selected does not matter in this situation.
The combination formula for selecting r items from a larger set of n items is given by:
C(n, r) = n! / [r! * (n - r)!]
Where ! denotes a factorial, the product of all positive integers up to that number.
In this case, we want to select 3 colors (r = 3) from the 6 available colors (n = 6). Plugging these values into the combination formula we have:
C(6, 3) = 6! / [3! * (6 - 3)!] = (6 * 5 * 4) / (3 * 2 * 1) = 20
Therefore, there are 20 different ways to select three colors for the printing job.