Question

A restaurant patron is making a salad. His salad can consist of just lettuce, or he can add any of the following items: carrots, sunflower seeds, mushrooms, cheese, onions, olives, tomato’s, pickles, bananas peppers, green peppers. How many different variations of a salad are possible?

Answer 1

There are 1024 different possible variations of salad.

How to determine the number of ways?

The number of ways of selecting at least one item from a list of distinct items can be calculated as:

$2^n -1$

Where n = number of distinct items in the list.

The items which could be added are:

{banana pepper, green peppers, onions, cucumbers, carrots, olives, pickles, cheese, sunflower seeds, tomatoes}

The number of items, n = 10

Therefore, the number of different variations of items that can be made from the list is :

$2^{10} - 1 = 1024 -1\\\\= 1023$

Since the salad originally contains lettuce only,

1023 + 1 = 1024

Hence, there are 1024 different variations of salad possible.

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