You grab an empty plate at the Ohkay Casino buffet. There are 27 different items

Question

You grab an empty plate at the Ohkay Casino buffet. There are 27 different items in the buffet, and you can have any combination of these items (including nothing at all), but you can only have one serving of any one thing. How many different possible combinations are possible?

You are the owner of the Rocky Mountain Candy Company and you will be assigning a unique 'candy code' to each type of candy you make. You make 758 different candy products. Each character in the candy code will be chosen from the following list: A,E,I,O,U,Y,4. How long does the candy code need to be in order to be able to assign a unique code to each type of candy? Another way of putting it is... what is the minimum number of 'slots' needed in the code?

There are 6 different organic vegetables on the table: 1 cucumber, 1 squash, 1 tomato, 1 lettuce, 1 artichoke and 1 pepper. You are to choose any 4 veggies to chop up and make a nice soup with. How many truly unique soups can you make?

Explanation / Answer

Q: You grab an empty plate at the Ohkay Casino buffet. There are 27 different items in the buffet, and you can have any combination of these items (including nothing at all), but you can only have one serving of any one thing. How many different possible combinations are possible?

A: every item has 2 choices associated with them, either to take it or not to take it.

so total combinations = 2^(27)

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