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Permutation Calculator (nPr)

Calculate the number of ways to arrange r items from n items where order matters.

Calculate P(n, r)

n (total items)

r (items to arrange)

Step-by-Step Solution

Formula

P(n, r) = n! / (n - r)!

Also written as nPr, P(n,r), or _nP_r

When to Use Permutations

Use Permutations When...

• Order matters (ABC ≠ CBA)
• Arranging items in a specific sequence
• Selecting president, VP, secretary
• Arranging books on a shelf

Use Combinations When...

• Order doesn't matter (ABC = CBA)
• Selecting a group or committee
• Choosing lottery numbers
• Picking pizza toppings

Common Permutation Examples

5 people in a row

P(5, 5) = 120

Gold, Silver, Bronze from 10

P(10, 3) = 720

3-letter codes from alphabet

P(26, 3) = 15,600

Frequently Asked Questions

What's the difference between permutation and combination?

In permutations, order matters (ABC is different from CBA). In combinations, order doesn't matter (ABC is the same as CBA). Permutations always give a larger result: P(n,r) = C(n,r) × r!

What is P(n, n)?

P(n, n) = n! This represents all possible arrangements of n items. For example, 5 people can be arranged in a row in 5! = 120 ways.

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Combination Calculator Factorial Calculator Probability Calculator Binomial Probability

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