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Advanced calculator for permutations, combinations, and arrangement problems with detailed solutions
Calculate arrangements and selections from a set
Total number of items available
Number of items to choose/arrange
Expert answers to common questions about permutations and combinations
Permutation is used when order matters (ABC ≠ BAC), like race positions or passwords. Combination is used when order doesn't matter (ABC = BAC = CAB), like lottery numbers or team selection.
Permutation P(n,r) = n! / (n-r)! where n is total items and r is items to arrange. For example, P(5,3) = 5!/(5-3)! = 120/2 = 60 ways.
Combination C(n,r) = n! / (r! × (n-r)!) where n is total items and r is items to select. For example, C(5,3) = 5!/(3!×2!) = 10 ways.
Use permutation when order matters: passwords, race rankings, seating arrangements. Use combination when order doesn't matter: lottery tickets, team selection, committee members.
Permutation with repetition allows items to be reused. Formula: n^r. For example, a 4-digit PIN from 10 digits = 10^4 = 10,000 possibilities.