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 $\boxed{{\displaystyle 65535}}$.