If there are three yellow, four black, six red, two green and six purple balls. If one wants five balls, how many ways are there to pick one out of each color?
Spontaneously I think about the multinomial coefficient
$\displaystyle\frac{n!}{k_1!k_2!\cdots k_m!}$ Where $k_1$ is, for instance, three yellow, and $k_m$ is four black.
Thus, $\displaystyle\frac{21}{3!4!6!2!6!}$. It does not seem to be right though.
Best Answer
Your given result,
Now let's focus on the question. Suppose balls of same color are distinct or marked.
Suppose balls of same color are identical or they cannot be distinguished from one another.