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?

Printable View

- Apr 10th 2013, 07:19 PMtesttrail429How 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? - Apr 10th 2013, 08:08 PMGusbobRe: How many options at the salad bar?
The prime factorisation is $\displaystyle 32,767=7\times 31 \times 151$. What does this tell you about the possible number of items?

- Apr 10th 2013, 08:32 PMSorobanRe: How many options at the salad bar?
Hello, testtrail429!

Quote:

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: .$\displaystyle 2^{15} = 32,768$ different decisions you can make.

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

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