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#Element of mathematics • #permutations_and_combinations • #maths • #Element book exercise 6.1 • #permutation • #lalit sir • #CNR CLASSES • #mathematics class 11 • #Class 11th • #applied mathematics • • Welcome to cnr classes, your go-to destination for mastering permutations and combinations! • In this channel, we'll explore the fascinating world of combinatorics, demystifying the concepts of permutations and combinations through: • Clear explanations • Engaging animations • Real-world examples • Practice problems and solutions • From understanding the fundamentals of permutations and combinations to applying them in various fields like mathematics, statistics, computer science, and data analysis, we've got you covered. • Join us on this journey to develop your problem-solving skills, enhance your mathematical understanding, and become proficient in permutations and combinations. • Subscribe now and let's unravel the possibilities together! • Feel free to customize it according to your channel's tone and style! • Permutations and combinations are fundamental concepts in mathematics, particularly in the field of combinatorics. • *Permutations*: • A permutation is an arrangement of objects in a specific order. The formula to calculate the number of permutations is: • P(n, r) = n! / (n-r)! • where: • n = total number of objects • r = number of objects to be arranged • ! denotes the factorial function (e.g., 5! = 5 × 4 × 3 × 2 × 1) • *Combinations*: • A combination is a selection of objects without regard to order. The formula to calculate the number of combinations is: • C(n, r) = n! / (r! × (n-r)!) • where: • n = total number of objects • r = number of objects to be selected • ! denotes the factorial function • Key differences: • Permutations consider the order of objects, while combinations do not. • Permutations are used when the arrangement of objects matters, whereas combinations are used when the selection of objects is what matters. • Example: • Permutation: Arrange 5 books on a shelf (order matters) • Combination: Select 3 books from a shelf (order doesn't matter) • Let me know if you have specific questions or need help with problems related to permutations and combinations!

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