SOLUTION: A fast food restaurant specializes in hame sandwiches. A customer may choose to add any of the following: mayonnaise, mustard, lettuce, tomato, or cheese. How many different ham sa

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Question 1183336: A fast food restaurant specializes in hame sandwiches. A customer may choose to add any of the following: mayonnaise, mustard, lettuce, tomato, or cheese. How many different ham sandwich combinations are possible?
(Note: The answer is 32, which is solved by doing 2^5; However, I do not understand the logic and reasoning behind simply getting 2 and raising it to the power of 5 rather than treating the problem as a series of multiple permutations of 5!*4!*3!*2!*1!*0!)
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!

There are two ways to decide regarding mayonnaise, you either want some or not. Same thing with each of the other ingredients, you either want some or not. So two ways to decide about mayo, times two ways to decide about mustard, etc.

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52795)   (Show Source):
You can put this solution on YOUR website!
.

I'd like to add my 2 cents regarding your note, where you write for a series of 5 permutations

                5!*4!*3!*2!*1!*0!

It is written incorrectly. The number of permutations of 5 items is

                5! = 5*4*3*2*1 = 120.

Be accurate, when you write Math ( ! )

Every word and every symbol matters . . .