How to calculate number of combinations for this problem? The problem is as follows:
You have an unlimited number of marbles and each marble is one of 16 different colours. You have to choose 6 marbles and order is irrelevant. How many different combinations of 6 marbles are there?

Let's think that we have $16$ boxes of different colors and $6$ equal marbles to distribute among the boxes to color them.
Now let's call $m$ to the marbles and consider $16-1=15$ "separators" s. The problem comes down to finding the number of anagrams of the word with $15+6=21$ letters, $6$ of them $m$ and other $15$ are $s$.
The answer is $\dfrac{21!}{15!.6!}=\binom{21}{15}$ because you have to select where to place the separators within the 21 total spaces and then in the remaining places to place the marbles.
For example, the word $m-m-s-s-s-s-m-s-s-s-s-s-m-m-s - m -s -s -s -s-s $ returns $2$ marbles with color $1$, $1$ marble with color $5$, $2$ marbles with color $10$ and $1$ marble with color $11$.
