Math Problem Statement
6Pn=360
Solution
To solve the equation , we need to understand that represents the number of permutations of 6 objects taken at a time.
The formula for permutations is given by:
We are given that , so:
Let's calculate (which is the factorial of 6):
Now, we can set up the equation:
Next, solve for :
Now, we need to find which factorial equals 2:
This means implies .
So:
Now, solve for :
Final Answer:
The value of is 4.
Would you like to see more details or have any other questions? Here are some related questions you might find interesting:
- What would the equation look like if ?
- How do you calculate permutations for larger values of ?
- How are permutations different from combinations?
- Can you use permutations in probability calculations?
- What if the permutation was ? How would you solve it?
Tip: When solving permutation problems, breaking down the factorials into smaller components can make it easier to find the solution.
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Math Problem Analysis
Mathematical Concepts
Permutations
Factorials
Formulas
Permutations formula: nPr = n! / (n-r)!
Theorems
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Suitable Grade Level
High School