MHB How many possible lunch special combinations can be ordered

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To determine the total number of lunch special combinations at Deb's Deli, customers can choose either a sandwich with a salad or a sandwich with a soup. There are 5 sandwich options, 4 salad options, and 3 soup options available. The quickest way to calculate the combinations is to use the fundamental counting principle, which involves multiplying the number of sandwich choices by the total number of item choices (salad and soup combined). This results in the equation N = 5(4 + 3), leading to a total of 35 possible combinations. Understanding this approach can help clarify combination questions for GRE preparation.
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Hi All, I'm studying for the GRE, and really struggling with combination questions for some reason. I'm posting here quite a bit, but just wanted to say thank you so much for your help.

What would be the fastest way to solve the following?

"At Deb's Deli, a customer may choose either a sandwich and a salad or a sandwich and a soup for the lunch special. There are 5 choices of sandwich, 4 choices of salad, and 3 choices of soup. How many possible lunch special combinations can be ordered"
 
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greprep said:
Hi All, I'm studying for the GRE, and really struggling with combination questions for some reason. I'm posting here quite a bit, but just wanted to say thank you so much for your help.

What would be the fastest way to solve the following?

"At Deb's Deli, a customer may choose either a sandwich and a salad or a sandwich and a soup for the lunch special. There are 5 choices of sandwich, 4 choices of salad, and 3 choices of soup. How many possible lunch special combinations can be ordered"

One way would be to compute the number of possible sandwich/salad combinations are possible, then compute the number of sandwich/soup combinations are possible, and then add the two to get the total. Or, you could do it in one pass by looking at it as a sandwich/item problem, where you have 5 choices for sandwich and 7 choices for item (salad or soup) and apply the fundamental counting principle.

What do you get?
 
Would it then just be 5x4x3, according to the fundamental counting principal?
 
greprep said:
Would it then just be 5x4x3, according to the fundamental counting principal?

No, not quite...you have 5 sandwich options, and then for the second option, you have 3 + 4 options:

$$N=5(4+3)=\,?$$
 

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