Math Problem Statement
A restaurant serves custom-made omelets, where guests select meat, cheese, and vegetables to be added to their omelet. There are 6 vegetables available, and guests may select any 2 vegetables for their omelet. How many different combinations of 2 vegetables are possible?
Solution
To solve this problem, we need to calculate the number of combinations of 2 vegetables that can be selected from the 6 available vegetables.
This is a combination problem, which is calculated using the formula:
Here:
- is the total number of items (6 vegetables),
- is the number of items to select (2 vegetables).
Substitute and :
The cancels out, leaving:
Answer: There are 15 different combinations of 2 vegetables possible.
Would you like further explanation or examples?
Here are 5 related questions:
- How many combinations are possible if guests could select 3 vegetables instead of 2?
- What is the formula for determining permutations instead of combinations?
- How would the result change if there were 8 vegetables instead of 6?
- Can you explain the difference between combinations and permutations?
- How many ways can guests select 1 vegetable out of 6?
Tip: Use combinations when the order of items doesn’t matter, and permutations when it does.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Counting Principles
Formulas
C(n, r) = n! / [r! * (n - r)!]
Theorems
Combination formula
Suitable Grade Level
Grades 8-10