A sandwich shop has the advertising slogan, “10,000 different sandwiches & one little eatery”. The shop offers its sandwiches with various combinations of mustard, catsup, mayonnaise, Cajun spice, relish, pickles, tomatoes, and lettuce. Customers can also choose between, turkey, salami, roast beef, ham and pastrami. The breads offered are whole wheat, sourdough, and dark rye and they can choose between American and Swiss cheeses. Is the ad truthful? Explain why or why not.
I am having a really hard time with this one. I know its a combination but fot the life of me I am unable to figure out how to work the problem.
The number of different combinations can be found by multiplying together the number of possibilities for each factor. (i.e. There are 5 types of meat)
so would I do the 3 choices of bread like 3x2x1=6 and then the meat 5x4x3x2x1=120 and then add them all together?
Also figure in one or more of these: various combinations of mustard, catsup, mayonnaise, Cajun spice, relish, pickles, tomatoes, and lettuce. A customer might choose one, some or all of these.
that did not help at all I need clarification. How is this supposed to be done.
To determine whether the ad is truthful, we need to calculate the number of different sandwich combinations that are possible based on the given options.
Let's break down the possibilities step by step:
1. Choice of condiments: There are 8 different condiments listed (mustard, catsup, mayonnaise, Cajun spice, relish, pickles, tomatoes, and lettuce). Note that each condiment can either be included or excluded from the sandwich. This means we have 2 choices (include or exclude) for each of the 8 condiments. So the total number of condiment combinations is 2^8 = 256.
2. Choice of meats: There are 5 different meats listed (turkey, salami, roast beef, ham, and pastrami). Again, each meat can either be included or excluded from the sandwich, giving us 2 choices for each meat. Hence, the total number of meat combinations is 2^5 = 32.
3. Choice of bread: There are 3 types of bread listed (whole wheat, sourdough, and dark rye). Since we can only choose one type of bread, the total number of bread combinations is simply 3.
4. Choice of cheese: There are 2 types of cheese listed (American and Swiss). Similar to the bread, we can only choose one type of cheese, so the total number of cheese combinations is 2.
To find the total number of sandwich combinations, we need to multiply the number of options for each category: 256 (condiments) × 32 (meats) × 3 (breads) × 2 (cheeses) = 491, 520 possible combinations.
Therefore, the ad's claim of "10,000 different sandwiches" is not truthful since there are only 491,520 possible combinations based on the given options.
I hope this explanation helps! Let me know if you have any further questions.