Math Calculators
Permutation & Combination Calculator
Calculate permutations and combinations using factorials.
What is the Permutation & Combination Calculator & How does it work?
Permutations, denoted as P(n,r), are the number of ways to arrange r items from a set of n items where order matters. Combinations, denoted as C(n,r), are the number of ways to choose r items from a set of n items without regard to order.Use permutations when the sequence of selection is important, such as arranging people in a line. Use combinations when the sequence does not matter, like selecting a team from players.
P(n,r) = frac{n!}{(n-r)!},quad C(n,r) = frac{n!}{r!(n-r)!}
n = total items, r = items to choose, ! = factorial
Parameters
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Permutations (P(n,r))
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Combinations (C(n,r))
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Frequently Asked Questions
What is the difference between permutations and combinations?
Permutations are for arranging items where order matters, while combinations are for selecting items where order doesn't matter.
How do I calculate permutations?
Use the formula P(n,r) = n! / (n-r)! where n is the total number of items and r is the number of items to arrange.
Can you explain how combinations work?
Combinations use the formula C(n,r) = n! / [r!(n-r)!] to calculate the number of ways to choose r items from a set of n without regard to order.
When should I use permutations instead of combinations?
Use permutations when the sequence of selection is important, such as arranging people in a line.
What does 'n' represent in permutation and combination formulas?
'n' represents the total number of items in the set from which you are selecting or arranging.
How do I calculate permutations for 5 items taken 3 at a time?
P(5,3) = 5! / (5-3)! = 60. There are 60 ways to arrange 3 items from a set of 5 when order matters.
Can you show me how to calculate combinations for 10 items taken 4 at a time?
C(10,4) = 10! / [4!(10-4)!] = 210. There are 210 ways to choose 4 items from a set of 10 when order doesn't matter.
Results are for informational purposes only and do not constitute professional advice.