Question 1043004
<pre>
That's: 
4 appetizers choose 3, = 4C3
and
6 main courses choose 3, = 6C3
and
7 desserts choose 6, or 7C6.

"And" means "times", so the answer is

(4C3)(6C3)(7C6) = (4)(20)(7) = 560 ways.

Edwin</pre>