Question
A chef has lettuce and ten other salad ingredients in stock. The chef is interested in counting how many salads could be created if they add five of the other ten ingredients to the lettuce. Decide if this is a permutation or combination problem. Select the two options below that indicate which type of problem this is. Select all that apply: To solve this problem, we want to list ingredients so order will matter. \( \square \) To solve this problem, we will group certain ingredients so order will not matter. \( \square \) This is a combination problem. We are grouping possibilities and order does not matter. This is a permutation problem. We are listing the possibilities and order does matter. The Ther
Ask by Ayala Sullivan. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
This is a combination problem because the order of ingredients does not matter when making salads.
Solution
The problem is asking how many salads can be made by choosing five of ten ingredients (in addition to lettuce, which is always included). Since the order in which the ingredients are chosen does not affect the salad, we are simply grouping ingredients without regard for order.
Thus, this is a combination problem. The two statements that apply are:
• To solve this problem, we will group certain ingredients so order will not matter.
• This is a combination problem. We are grouping possibilities and order does not matter.
Since the order does not matter, it is not a permutation problem.
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Simplify this solution The Deep Dive
When choosing salad ingredients, the order in which ingredients are selected doesn’t affect the final salad outcome, making this a classic combination problem! You could toss the ingredients in any order and the salad would still taste delicious—lettuce loves company, regardless of how it’s plated! In real life, think about how you create salads at home. You don’t meticulously arrange the ingredients in a specific order; instead, you grab and mix your favorites! This is similar to the mathematical concept of combinations, which helps chefs (and home cooks) explore all the delightful ways to mix flavors without fussing over the arrangement.
