A deli offers its cheese sandwich with various combinations of mayonnaise, lettuce, tomatoes, pickles, and sprouts. 8 types of cheese are available. How many different cheese sandwiches are possible?
Assuming you can have one and only one type of cheeze (i.e., no provolone and swiss sandwiches allowed), and assuming you cannot get extra toppings (e.g, no sandwich with extra mayo allowed)....
There are 8 type of cheese and 5 toppings. With each topping, there are 2 possible answers, either yes or no.
So 8*(2^5) = 256.
Thank you, that helped out a lot!
To find the number of different cheese sandwiches possible, we need to multiply the number of options for each component of the sandwich.
We have 8 types of cheese available for the sandwich. Let's call this C.
Next, let's consider the condiments: mayonnaise, lettuce, tomatoes, pickles, and sprouts. For each condiment, we have two options: either it is present in the sandwich or it is not. Let's call this option P for present, or N for not present.
Therefore, for each condiment, we have 2 options. Since there are 5 condiments, we need to multiply 2 by itself 5 times (2^5) to calculate the number of options for condiments.
Finally, we multiply the number of cheese options by the number of condiment options:
8 (cheese options) multiplied by 2^5 (condiment options) equals 8 * 2^5.
Calculating this equation: 8 * 2^5 = 8 * 32 = 256.
Therefore, there are 256 different cheese sandwiches possible at the deli.