Combinatorics - Restaurant Menu!!

kunalkulkarni wrote: A restaurant menu features five appetizers, six entrees, and three desserts. If a dinner special consists of two appetizers, two entrees, and two desserts, how many different dinner specials are possible?

Take the task of "building" a meal and break it into stages.

Stage 1: Select 2 appetizers.
Since the order of the selected appetizers does not matter, we can use combinations here.
We can select 2 appetizers from 5 appetizers in 5C2 ways (10 ways).

Aside: If anyone is interested, we have a free video on calculating combinations (like 5C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Stage 2: Select 2 entrees.
Once again, the order of the selected entrees does not matter, so we can use combinations.
We can select 2 entrees from 6 entrees in 6C2 ways (15 ways).

Stage 3: Select 2 desserts.
We can select 2 desserts from 3 desserts in 3C2 ways (3 ways).

By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus create a meal) in (10)(15)(3) ways ([spoiler]= 450 ways[/spoiler])

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775