Choosing Exactly $$r$$ from Multiple Groups

Choosing Exactly $$r$$ from Multiple Groups

## Formula

If $$r$$ objects are selected from groups containing $n_1,n_2,\ldots,n_k$ objects, then:

$$\sum_{r_1+r_2+\cdots+r_k=r}{}^{n_1}C_{r_1}{}^{n_2}C_{r_2}\cdots{}^{n_k}C_{r_k}$$

## Usage

- Used when the number selected from each group can vary but the total number selected is fixed.