![]() ![]() Number of combinations of n distinct things taking r at a time ( nC r) can be given by Number of Combinations of n distinct things taking r at a time If the order is not important, problem will be related to combinations.įor permutations, the problems can be like "What is the number of permutations the can be made", "What is the number of arrangements that can be made", "What are the different number of ways in which something can be arranged", etc.įor combinations, the problems can be like "What is the number of combinations the can be made", "What is the number of selections the can be made", "What are the different number of ways in which something can be selected", etc.ġ0. ![]() If the order is important, problem will be related to permutations. If order is not important, PQ will be same as QP, PR will be same as RP and QR will be same as RQ If order is important, PQ will be different from QP, PR will be different from RP and QR will be different from RQ To understand if the question is related to permutation or combination, we need to find out if the order is important or not. However if it is not mentioned in the problem, we have to find out whether the question is related to permutation or combination.Ĭonsider a situation where we need to find out the total number of possible samples of two objects which can be taken from three objects P, Q, R. ![]() Sometimes, it will be clearly stated in the problem itself whether permutation or combination is to be used. Difference between Permutations and Combinations and How to identify them The absolute value or modulus of a complex number z = a + b i z=a+bi can be interpreted as the distance of the point ( a, b ) (a,b) from the origin on a complex plane. The complex number a + b i a+bi can be plotted as the ordered pair ( a, b ) (a,b) on the complex plane. When we use the Cartesian plane this way, we call it the complex plane. We can graph a complex number on the Cartetian plane using the horizontal axis as the real axis and the vertical axis as the imaginary axis. In a complex number z = a + b i z=a+bi, a a is called the "real part" of z z and b b is called the "imaginary part." If b = 0 b=0, the complex number is a real number if a = 0 a=0, then the complex number is "purely imaginary." No:11 SAQ complex numbers Complex NumbersĪ complex number is a number of the form a +ib , where a and b are real numbers and i is the Imaginary number, the square root of i is −1. Random Variables and Probability Distributions Unit 10 : Random Variables and Probability Distributions ![]()
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