A restaurant patron is making a salad. His salad can consist of just lettuce, or he can add any of the following items: cheese, mushrooms, olives, tomatoes, sunflower seeds, green peppers, carrots. How many different variations of a salad are possible?
There are variations of a salad possible. (Simplify youranswer.)
n example Get more help.
Clear all
Final Answer: The number of different variations of a salad are possible is \(\boxed{127}\).
Step 1 :The problem is asking for the number of combinations of salad ingredients. This is a combinatorics problem.
Step 2 :The patron can choose to include or not include each ingredient, so there are 2 choices for each ingredient.
Step 3 :Since there are 7 ingredients, the total number of combinations is \(2^7\).
Step 4 :However, the problem states that the salad can consist of just lettuce, so we need to subtract 1 from the total to exclude the case where no ingredients are added.
Step 5 :total_combinations = 127
Step 6 :Final Answer: The number of different variations of a salad are possible is \(\boxed{127}\).