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Permutations Formula (nPr)
Algebra • Grades 9, 10, 11, 12
Algebra
Permutations Formula (nPr)
Calculate ordered arrangements of items with P(n, r) = n! / (n - r)!.
The Formula
P(n,r) = n! / (n-r)!
Used for: Counting the number of ordered arrangements of r items chosen from a set of n items
nTotal number of items available
rNumber of items arranged in order
n!Factorial notation
⚡Live Interactive Quick Solver
Instant CalculationPermutations P(7, 3):210 arrangements
Formula: 7! / (4!) = 210
P(n, r) = \frac{n!}{(n - r)!}
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
🔢
Order Matters!Arranging positions 1st, 2nd, 3rd where (A, B) ≠ (B, A).
❗
P(n, r) = n! / (n - r)!Number of permutations of n items taken r at a time.
📝 Worked Examples & Step-by-Step Solutions
Example 1: Race with 8 Runners
Problem:
How many ways can 1st, 2nd, and 3rd place be awarded among 8 runners?1
Identify
n = 8, r = 32
Apply Formula
P(8, 3) = 8! / (8 - 3)! = 8! / 5!3
Expand
8 × 7 × 6 = 336Answer: 336 ways
💡 Pro Tips & Common Mistakes
Permutation vs Combination
Use permutations when order or position matters (e.g. passwords, races).
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