Check my work please?

If I have 7 men and 9 women, and I am making a guest list that will consist of 5 men and 5 women. How many different ways can I chose who I invite?

I think that for the men, its 7 choose 5, and for the women 9 choose 5.

Since order doesn't matter, I think that I just add these two right?

Question

Check my work please?

If I have 7 men and 9 women, and I am making a guest list that will consist of 5 men and 5 women. How many different ways can I chose who I invite?

I think that for the men, its 7 choose 5, and for the women 9 choose 5. 

Since order doesn't matter, I think that I just add these two right?

anonymous · Answer

so I have $$\left(\begin{matrix}7 \ 5\end{matrix}\right) + \left(\begin{matrix}9 \ 5 \end{matrix}\right)$$ which is 147.

anonymous · Answer

Actually, you multiply those

anonymous · Answer

ah shoot, basic principle of counting eh?

anonymous · Answer

So, 2646 unique lists.

anonymous · Answer

The reasoning is that for every grouping of one gender, you have available the full gamut of all the other gender's possibilities.

anonymous · Answer

Yes, you got it!  Good job!

anonymous · Answer

All good now, @xartaan ?

anonymous · Answer

Ya thanks, very clear, I appreaciate it!

anonymous · Answer

uw!  Good luck to you in all of your studies and thx for the recognition! @xartaan