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a deli offers it's cheese sandwich with various combinations of mayo,lettuce, tomatoes, pickles and sprouts. 5 different types of cheese are avaiable. How many different chesse sandwiches are possible?

  • math -

    with the 5 condiments listed there would be 2^5 subsets or 32 different ways to have the condiments, including none and all of them

    so the number of different sandwiches
    = 32 x 5 ways
    = 160

    (this assumes that only one kind of cheese is on a sandwich.
    If multiple cheeses can go on, there would be 2^10 -1 or 59048 ways to have the cheeses.
    I subtracted 1 to exclude 'no cheeses'. Having a cheese sandwich without cheese is a contradiction.)

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