Question

Three research departments have 10, 9, and 8 members, respectively. Each department is to select a delegate and an alternate to represent the department ata conference. In how many ways can this be done?

Answer 1

Start by findind in how many ways it can be done for each department using combinations in each way

$\begin{gathered} 10C2=45 \\ 9C2=36 \\ 8C2=28 \end{gathered}$

then since there is an addition we must multiply each of those posibilities

$45\cdot36\cdot28=45360$

It can be done in 45360 ways