A deli offers its cheese sandwich with various combinations of mayonnaise, lettuce, tomatoes, pickles, and sprouts. 5 types of cheese are available. How many different cheese sandwiches are possible?
I got 10 for the answer is that correct?
Not that simple.
First of all, your question is not totally clear.
Can you have more than one of the condiments, e.g. lettuce and tomatoes and pickles?
Secondly, can you have more than one type of cheese?
I will assume the above.
There are 2^5 or 32 subsets of the 5 condiments, including none of them
There are 2^5 -1 or 31 ways to have a cheese combination. (I subtraced 1 since a no-cheese sandwich is not a "cheese sandwich")
So the number of different cheese sandwiches is
32 x 31 or 992
Below is the problem again with the answer choices....
A deli offers its cheese sandwich with various combinations of mayonnaise, lettuce,tomatoes,pickles, and sprouts. 5 types of cheese are available. How many different cheese sandwiches are possible?
Answer choice:
a)320 b)80 c)160 d)10
Again, the question does not clear up the problem I stated.
The only logical answer I can see is 160, but that would assume that we can have multiple combinations of the condiments but only 1 kind of cheese.
namely 32 x5 = 160
But...
why can't a cheese sandwich have more than one kind of cheese?
so go with the 160
I ask my self the same question the reason i was getting confused... Thanks so much
To determine the number of different cheese sandwiches that are possible, you need to consider the options for each ingredient: mayonnaise, lettuce, tomatoes, pickles, and sprouts.
Since the question only mentions the types of cheese and not the quantity, it is safe to assume that you can choose any number of cheese types for each sandwich.
Let's break it down:
1. Mayonnaise: You have two choices - either to include it or not. So, there are 2 possibilities for mayonnaise.
2. Lettuce: Again, you have two choices - to include it or not. There are 2 possibilities for lettuce.
3. Tomatoes: You have two choices - to include them or not. There are 2 possibilities for tomatoes.
4. Pickles: Two choices - to include them or not. There are 2 possibilities for pickles.
5. Sprouts: Two choices - to include them or not. There are 2 possibilities for sprouts.
Now let's consider the types of cheese. Since there are 5 types of cheese available and you can choose any number of cheese types for each sandwich, we can either include a specific type of cheese or exclude it. This gives us 2 possibilities for each type of cheese.
So, the total number of different cheese sandwiches that are possible is calculated by multiplying the number of possibilities for each ingredient:
2 (mayonnaise) x 2 (lettuce) x 2 (tomatoes) x 2 (pickles) x 2 (sprouts) x 2^5 (five types of cheese) = 2^8 = 256
Therefore, there are a total of 256 different cheese sandwiches that are possible with the given combinations of ingredients.