Posted by **Tracy** on Friday, April 16, 2010 at 9:29am.

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?

- math-HELP -
**Reiny**, Friday, April 16, 2010 at 10:26am
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

- math-HELP -
**Tracy**, Friday, April 16, 2010 at 10:34am
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

- math-HELP -
**Reiny**, Friday, April 16, 2010 at 10:43am
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

- math-HELP -
**nicole**, Friday, April 16, 2010 at 10:46am
I ask my self the same question the reason i was getting confused... Thanks so much

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