Math Problem Statement
how it was calculated
Solution
In the given example, the problem is to find the number of permutations of a set , which consists of 4 elements, taken 2 elements at a time.
Key Concepts:
- Permutation Formula: The number of ways to select and arrange elements from a set of elements is given by: where denotes the factorial of , which is the product of all positive integers up to .
Given:
- (since the set contains 4 elements: {1, 2, 3, 4}),
- (we are choosing 2 elements at a time).
Step-by-Step Calculation:
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Apply the formula:
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Evaluate the factorials:
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Substitute and divide:
Thus, the number of permutations is 12. This means there are 12 ways to arrange 2 elements out of the 4-element set.
Would you like more details or have any questions about this calculation?
Here are 5 related questions to expand your understanding:
- How would you calculate the permutations if instead of ?
- What is the difference between permutation and combination?
- How would you calculate combinations for the same values of and ?
- What is the significance of the factorial function in permutation and combination formulas?
- Can you explain how the arrangement changes if we are not allowed to repeat elements?
Tip: For larger values of , using factorials directly can become tedious, so factorial tables or calculators are often used for quicker results.
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Math Problem Analysis
Mathematical Concepts
Permutation
Factorials
Formulas
Permutation formula P(n, r) = n! / (n - r)!
Theorems
Permutation Theorem
Suitable Grade Level
Grades 9-12