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Answer :
Answer: 128
Step-by-step explanation:
Given : Total ingredients =7
When we select any one of ingredient for salad, then total choices for each ingredient = 2 (Yes or No)
So for all 7 ingredients there will be [tex]2\times2\times2\times2\times2\times2\times2=2^7=128[/tex] choices [By fundamental principle of counting]
Hence, there are 128 different salads are possible where two salads are different if they don't include identical ingredients
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Final answer:
There are 127 different possible salads that can be made from a selection of 7 ingredients at a salad bar, as calculated by the power set formula (2^7 - 1) excluding the empty set.
Explanation:
The question pertains to the number of different combinations that can be made with 7 ingredients at a salad bar. To determine this, we need to consider the principles of combinatorics. Since no ingredient can be used more than once in a single salad, we can use the formula for the power set, minus the empty set, to calculate the number of possible combinations. The power set formula is 2^n, where 'n' is the number of items to choose from, in this case, 7 ingredients. However, we subtract the empty set because at least one ingredient must be chosen for it to be considered a salad.
The calculation is therefore 2^7 - 1, which equals 128 - 1. Thus, excluding the empty set, there are 127 different possible salads that can be made when choosing from 7 different ingredients.
