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### Concepts, Problems and Solutions in Permutations, Combinations and Probability

Concepts, Problems and Solutions in Permutations, Combinations and Probability.

The present work is an arithmetic treatment of the principles of permutations, combinations and probability. This book contains a large number of examples for exercise, fully solved, which will serve as complete guide to private students reading the subject with few or no opportunities of instruction. Based on a purely arithmetic basis, the present elementary treatise will be intelligible to a reader who has no knowledge of mathematics and will put him into possession of the principles upon which simple questions of probability are determined. But while expressly written for unscientific readers, this will be very helpful to the young mathematician, who is about to read in the algebra the hitherto difficult and embarrassing chapters on permutations and combinations, or on probability.

Solutions are provided next to the exercises and examples throughout the book. This will save the time and lighten the work of Teachers as well. This book helps in acquiring a better understanding of the basic principles of Permutations, Combinations and Probability and in revising a large amount of the subject matter quickly. Care has been taken, as in the former Keys, to present the solutions in a simple natural manner, in order to meet the difficulties which are most likely to arise, and to render the work intelligible and instructive.

The examples have been selected with a view to illustrate every part of the subject, and, as the number of them is more than two thousand, I trust they will supply ample exercise for the student. Complicated and difficult problems have been excluded, because they consume time and energy which may be spent more profitably on other branches of mathematics. Each set of examples has been carefully arranged, commencing with some which are very simple and proceeding gradually to others which are less obvious. The detailed solutions to the examples are provided.

To provide room for more practice, more than one thousand problems are added at the end of this volume, all fully solved in the chapter titled Miscellaneous Problems.

This work contains several variations of problems, solutions, methods, approaches to enrich, strengthen and enliven the inherent multi-concepts.

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Chandra Shekhar Kumar

Chandra Shekhar Kumar is Staff Software Architect @ GE Healthcare (Ultrasound Digital Solutions). In an innovator role, he is actively involved in digital Innovation in Ultrasound ecosystem (premise, edge and cloud) including (but not limited to) C++17/20/23, Boost C++ Libraries, WineLib, Qt, wxWidgets, WebAssembly, NATS.io, Hashicorp Nomad and Rust. Motto is to build once and run everywhere using the same code base (using and extending WebAssembly Infrastructure)

He is Co-Founder of Ancient Science Publishers (estd.2014), a venture to publish monographs on mathematics, physics and computer science and render services related to hiring technical talents, training for competitive programming, algorithms, programming interviews, IITJEE and Olympiads. Inspiration for this undertaking came from the writings of Leonhard Euler (mathematics), Richard Phillips Feynman (physics) and Edsger Wybe Dijkstra (computer science).

https://ancientscience.github.io/

He is Founder of Ancient Kriya Yoga Mission (estd.2013), a venture to disseminate simple techniques of ancient science of living and publish kriya yoga scriptures and commentaries.

He holds a degree of Integrated M.Sc.(5 yrs) in Physics from IIT Kanpur.

He has worked with software companies like Trilogy, Oracle and few start-ups.

He has been programming in C++ for the last 22 years. He loves to hack gcc, gdb, valgrind, clang, boost, TeX, LaTeX and pours inside the works of Dijkstra and Knuth.

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