How many possible lunch special combinations can be ordered

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In summary, the question is asking how many possible combinations of sandwich, salad, and soup are available for the lunch special at Deb's Deli. One way to solve this is to compute the number of sandwich/salad combinations and sandwich/soup combinations separately and add them together. Another way is to view it as a sandwich/item problem and use the fundamental counting principle, where there are 5 sandwich options and 7 options for the second item (salad or soup). The total number of combinations is then 5x7=35.
  • #1
greprep
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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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  • #2
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?
 
  • #3
Would it then just be 5x4x3, according to the fundamental counting principal?
 
  • #4
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:

\(\displaystyle N=5(4+3)=\,?\)
 

1. How do you calculate the number of possible lunch special combinations?

The number of possible lunch special combinations can be calculated by multiplying the number of options for each component of the lunch special. For example, if there are 3 options for the main dish, 4 options for the side dish, and 2 options for the drink, the total number of combinations would be 3 x 4 x 2 = 24.

2. What factors influence the number of possible lunch special combinations?

The number of possible lunch special combinations is influenced by the number of options available for each component (main dish, side dish, and drink), as well as any restrictions or limitations set by the restaurant (e.g. no substitutions allowed).

3. Is there a limit to the number of possible lunch special combinations?

Technically, there is no limit to the number of possible lunch special combinations as long as there are different options for each component. However, in reality, there may be practical limitations such as the number of ingredients or resources available to the restaurant.

4. How does the number of possible lunch special combinations affect menu planning?

The number of possible lunch special combinations can greatly impact menu planning, as it affects the variety and options available to customers. A larger number of possible combinations allows for more flexibility and caters to different tastes and preferences.

5. Can the number of possible lunch special combinations be reduced?

Yes, the number of possible lunch special combinations can be reduced by limiting the options for each component or by setting certain restrictions or limitations. For example, a restaurant may offer a set menu with only a few options for each component, resulting in a smaller number of possible combinations.

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