Permutation Calculator
Calculate the number of permutations (ordered arrangements) when choosing r items from n items.
P(n, r)
720
P(n, r) vs Total Items (n)
公式
## How to Calculate Permutations ### Formula **P(n, r) = n! / (n - r)!** A permutation counts the number of ways to arrange r items chosen from n distinct items where order matters. For example, selecting a president, vice-president, and secretary from 10 people is a permutation problem because each position is different.
计算示例
How many ways can you arrange 3 books from a shelf of 10?
- 01P(10, 3) = 10! / (10 - 3)!
- 02= 10! / 7!
- 03= 10 * 9 * 8 = 720
- 04Compare with combinations: C(10,3) = 120 (order does not matter)
常见问题
What is the difference between permutation and combination?
Permutations count ordered arrangements (ABC is different from BAC), while combinations count unordered selections (ABC and BAC are the same group). P(n,r) = C(n,r) * r!.
What is P(n, n)?
P(n, n) = n!, which is the total number of ways to arrange all n items. For example, P(5,5) = 120.
Can r be larger than n?
No. You cannot choose more items than are available. P(n, r) is only defined for 0 <= r <= n.
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