Combinations from a food menu: "Restaurant offers burritos on corn or flour..."

earthman

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Combinations from a food menu: "Restaurant offers burritos on corn or flour..."

"A restaurant offers burritos on a corn or a flour tortilla, 5 types of meat, 6 types of cheese, and 3 different toppings. When ordering, customers can choose 1 type of tortilla, 1 meat, and 1 cheese. They can then add any of the 3 toppings. How many burrito combinations are possible?"


I started out thinking that there was a total of 4 different ways things could be arranged and that the number of different possible items to choose from was 16. But, then I hit a dead end. What am I missing? Is this a combination problem?

Thanks!
 
Let's say this is your regular lunch place. You want to have a different meal every day. How do you do it?
 
"A restaurant offers burritos on a corn or a flour tortilla, 5 types of meat, 6 types of cheese, and 3 different toppings. When ordering, customers can choose 1 type of tortilla, 1 meat, and 1 cheese. They can then add any of the 3 toppings. How many burrito combinations are possible?"

I started out thinking that there was a total of 4 different ways things could be arranged and that the number of different possible items to choose from was 16. But, then I hit a dead end. What am I missing? Is this a combination problem?

You're never choosing from all 16 items. First you choose one of 2 kinds of tortilla; then one of 5 kinds of meat; and so on. Remember the multiplication principle. And there's no "arranging" to do; order doesn't matter. None of it is permutation, or "combination" in the technical sense either.

You will want to be sure how to interpret "any of the 3 toppings". It could mean "any one of the toppings", but I think it means "choose whether to include each topping" (so you could have none, one, two, or all).

If you need more help, be sure to show specifically what you are trying, so we can check for errors. Don't just describe it in general.
 
what's the clue that this isn't a combination problem?

Let's say this is your regular lunch place. You want to have a different meal every day. How do you do it?

I would start by having every possible meal on a corn tortilla. I would choose a meat and a cheese. (Meat 1 and Cheese 1). I could do that for the next three days in a row because there are three toppings. Running total equal 3.

Then, I could do the same each of the remaining five types of cheese. That would be a running total of 18 days.

Then, I would have to move on to trying different kinds of meat. I would assume that if it took 18 days to do one kind of meat, then I could multiply 18 days by the total number of meats to find out how many days it would take to do the previous pattern for every kind of meat available. So that would be 5 times 18 for a total of 90 days to try every combination on a corn tortilla.

I would assume that I could then do the same pattern of events for flour tortillas in 90 days. So the total number of different meals would be 180 different meals.

Ok, so if that logic is correct, how am I supposed to know that this isn't a "combination" problem? TE=lev888;424292]Let's say this is your regular lunch place. You want to have a different meal every day. How do you do it?[/QUOTE]

I would start by having every possible meal on a corn tortilla. I would choose a meat and a cheese. (Meat 1 and Cheese 1). I could do that for the next three days in a row because there are three toppings. Running total equal 3.

Then, I could do the same each of the remaining five types of cheese. That would be a running total of 18 days.

Then, I would have to move on to trying different kinds of meat. I would assume that if it took 18 days to do one kind of meat, then I could multiply 18 days by the total number of meats to find out how many days it would take to do the previous pattern for every kind of meat available. So that would be 5 times 18 for a total of 90 days to try every combination on a corn tortilla.

I would assume that I could then do the same pattern of events for flour tortillas in 90 days. So the total number of different meals would be 180 different meals.

Ok, so if that logic is correct, how am I supposed to know that this isn't a "combination" problem?
 
You're never choosing from all 16 items. First you choose one of 2 kinds of tortilla; then one of 5 kinds of meat; and so on. Remember the multiplication principle. And there's no "arranging" to do; order doesn't matter. None of it is permutation, or "combination" in the technical sense either.

You will want to be sure how to interpret "any of the 3 toppings". It could mean "any one of the toppings", but I think it means "choose whether to include each topping" (so you could have none, one, two, or all).

If you need more help, be sure to show specifically what you are trying, so we can check for errors. Don't just describe it in general.
I was trying to skip the reasoning and use the combinations formula, which goes something like nCr = n!/r!(n-1)! or something like that. But, now I realize that this more about multiplication and counting than combinations. But, the word combination is right in the problem. So I am confused about how I should know that this isn't a combination question.
 
suppose picking toppings is optional

"A restaurant offers burritos on a corn or a flour tortilla, 5 types of meat, 6 types of cheese, and 3 different toppings. When ordering, customers can choose 1 type of tortilla, 1 meat, and 1 cheese. They can then add any of the 3 toppings. How many burrito combinations are possible?"

Suppose picking toppings is optional. Would the number of possible burritos be:

(2)types of tortillas(5)types of meat(6)types of cheese(2)yes or no topping 1(2)yes or now topping 2(2) yes or no topping 3= 2x5x6x2x2x2=360?
 
I was trying to skip the reasoning and use the combinations formula, which goes something like nCr = n!/r!(n-1)! or something like that. But, now I realize that this more about multiplication and counting than combinations. But, the word combination is right in the problem. So I am confused about how I should know that this isn't a combination question.

Basically, you just have to ignore the fact that they happen to use the word "combinations"; they are using it in an informal sense, not using the formal definition. Word problems are generally not written in math but in everyday English; so you focus on what is happening and let that, not the words, dictate what you do.

"A restaurant offers burritos on a corn or a flour tortilla, 5 types of meat, 6 types of cheese, and 3 different toppings. When ordering, customers can choose 1 type of tortilla, 1 meat, and 1 cheese. They can then add any of the 3 toppings. How many burrito combinations are possible?"

Suppose picking toppings is optional. Would the number of possible burritos be:

(2)types of tortillas(5)types of meat(6)types of cheese(2)yes or no topping 1(2)yes or now topping 2(2) yes or no topping 3= 2x5x6x2x2x2=360?

Yes, that is the answer to the question as I took it, "choose whether to include each topping (so you could have none, one, two, or all)" -- except that the product is not 360).
 
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