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Math Help - How many options at the salad bar?

  1. #1
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    How many options at the salad bar?

    A restaurant advertises that its salad bar offers 32,767
    different combinations of items for its customers. How many
    items are included in its salad bar?
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  2. #2
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    Re: How many options at the salad bar?

    The prime factorisation is 32,767=7\times 31 \times 151. What does this tell you about the possible number of items?
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  3. #3
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    Re: How many options at the salad bar?

    Hello, testtrail429!

    A restaurant advertises that its salad bar offers 32,767 different combinations
    of items for its customers. .How many items are included in its salad bar?

    There are 15 items in the salad bar.


    Justification:

    For each item, you have a choice: yes or no.

    Hence, there are: . 2^{15} = 32,768 different decisions you can make.

    But one of them is "no" to all 15 items (you are not a customer).

    Therefore, there are: . 32,\!768-1 \,=\,32,\!767 choices.
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