Combinatorics Discrete Mathematics (Part-1) Study Notes- Combinatorics topic comes under discrete mathematics is divided in into 2 parts first part includes Sum Rule, Product Rule, Permutation, Combination.
This topic is important for various competitive exams such as GATE CSE, SSC JE, ISRO, ESE, IES and other computer science exams.
If a task can be done either in one of the n1 ways or in one of the n2 ways, where none of the set of n1 ways is the same as any of the set of n2 ways, then there are n1 + n2 ways to do the task.
Suppose that a procedure can be broken down into a sequence of two tasks. If there are n1 ways to do the first task and for each of these ways of doing the first task, there are n2 ways to do the second task, then there are n1n2 ways to do the procedure.
Permutation in Combinatorics
A permutation of a set of distinct objects is an ordered arrangement of these objects.
The number of permutations of n-objects:
Combination in Combinatorics
An r-combination of elements of a set is an unordered selection of r elements from the set.
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