Question

please help.....
A committee of six people is chosen from six senators and eight representatives. how many committees are possible if there are to be three senators and three representatives on the committee?

Answer 1

you want 3 from the senators and 3 from the representatives.

Answer 2

since the order does not count that gives you
$$ {6 \choose 3 } \cdot { 8 \choose 3}
$$

Answer 3

so i'll have 2 solutions? compute the \[\left(\begin{matrix}6 \\ 3\end{matrix}\right)\] first then the \[\left(\begin{matrix}8 \\ 3\end{matrix}\right)\] and multiply the answers?

Answer 4

got it thanks :)