Permutation and Combination Calculator

Permutation and combination are fundamental concepts frequently used in probability and statistics. Permutation (P) counts arrangements where order matters, while combination (C) only concerns the selection itself. Permutation: Used when order is important. For example, how many different ways can you arrange 5 different books on a shelf? P(5,5) = 5! = 120. Formula: P(n,r) = n!/(n-r)!. If you want to arrange 3 people from a group of 10: P(10,3) = 10×9×8 = 720 different arrangements. Combination: Used when order doesn't matter. For example, how many different ways can you select a 3-person committee from 10 people? C(10,3) = 120. Formula: C(n,r) = n!/(r!×(n-r)!). Combination is always less than or equal to permutation because order is not counted. Application areas: Lottery and gambling (calculating winning probability), Genetics (DNA sequence combinations), Password creation (number of secure combinations), Team selection and tournament organization, Widely used in data analysis and machine learning.