Suppose you have 16 tubes of paint. How many distinct color groupings can you make with your paint?

Step 1 ：We are given 16 tubes of paint and asked to find the number of distinct color groupings we can make. This is a problem of combinations, where the order of grouping does not matter.

Step 2 ：The formula for combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where \(n\) is the total number of items, \(k\) is the number of items to choose, and \(!\) denotes factorial, which is the product of all positive integers up to that number.

Step 3 ：In this case, we are choosing groups from 16 tubes of paint, so \(n = 16\). The number of tubes in each group can vary from 1 to 16, so we need to calculate the sum of combinations for \(k = 1\) to 16.

Step 4 ：By calculating, we find that the total number of combinations is 65535.

Step 5 ：Thus, the number of distinct color groupings you can make with 16 tubes of paint is \(\boxed{65535}\).