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Permutation
Permutation Definition of Permutation: The arrangement of any finite number of objects or the given numbers in a certain order is called Permutation. Examples: 1) In how many ways can three letters A,B and C be arranged in a row taking all three at a time? Solution: In order to arrange the given three letters A,B,C taking all three at a time(without repetition) in the form of row; we have the following three choices to fill up the three letters in the first ,second and third places: Choice for letter in the first place = 3 ways Choice for letter in the second place = 2 ways Choice for letter in the third place = 1 way Now, using the basic principle of counting, Total no. of ways= 3x2x1 ...
Arithmetico-Geometric Series
Arithmetico-Geometric Series Definition : If each part of a series is the product of the terms of the terms of an arithmetic progression and the terms of a geometric progression, then the series is known as the Arithmetico-Geometric series. The terms of the arithmetic progression in the general form are:- a,a+d,a+2d,a+3d, ....... a+(n-1)d and The terms of a geometric progression are 1,r,r²,r³, ... then the series a.1+(a+d).r+(a+2d).r²+...............+a+(n-1)d.r^n is called the arithmetico-geometric series.
Cramer's Rule
1.Solution of System of 2-linear Equations using Cramer's Rule. Example-1 Formula: x=D1/D and y=D2/D 2.Solution of System of 3-linear Equations using Cramer's Rule. Example-2 Formula:x=D1/D, y=D2/D and z=D3/D Step- by-Step method
Exponential And Logarithmic Series
Exponential and Logarithmic Series Solved Examples Of Exponential and Logarithmic Series
Basic Principle Of Counting
Basic Principle Of Counting Definition: If first thing can be done independently in n1 different ways and 2nd thing can be done in n2 different ways and 3rd thing can be done in n3 ways and so on (for any finite number of things), then the total number of ways the whole thing can be done in n1*n2*n3*......ways.This is called the basic Principle of Counting. Example:1 In how many ways can a man travel from city A to city C, if he can go from city A to B in 3ways and from city B to city C in 2 ways? Solution: The no. of ways a man can travel from City A to B(n1)=3 ways The no. of ways a man can travel from City B to C(n2)=2 ways The no. of ways he can travel from City A to C ? Using the basic Principle of counting, Total no. of ways= n1Xn2 ...