I'm attempting a problem that is as follows:
In a bag full of fruits, $13\%$ are apples, $37\%$ are oranges, $20\%$ are bananas, $10\%$ are pears, and $20\%$ are avocados. Find the probability that $12$ randomly selected fruits are $3$ apples, $2$ oranges, $5$ bananas, $1$ pear, and $1$ avocado.
At first glance this looks like a hypergeometric problem if we pretend there are $100$ fruits in total inside the bag, where $p_{\text{fruit}}(x)=\frac{\binom{b}{x}\binom{r}{k-x}}{\binom{b+r}{k}}$. Where $p$ is the number of fruits in the bag, $x$ the number of a specific fruit we want, $r$ is the number of other fruits, and $k$ is the total number of fruits we are selects. for example $p_{\text{apples}}(3)=\frac{\binom{13}{3}\binom{100-13}{12-3}}{\binom{100}{12}}$. Then the desired probability would just be $p_{\text{apples}}(3)\ \ \ p_{\text{oranges}}(2)\ \ \ p_{\text{banana}}(5)\ \ \ p_{\text{pear}}(1)\ \ \ p_{\text{avocado}}(1)$. However I'm not sure if this is a valid move, so I'm wondering if there is such a thing as a multivariate hypergeometric that considers $k$ types of objects instead of just two.