discrete math counting cheat sheet

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This ordered or stable list of counting words must be at least as long as the number of items to be counted. of edges =m*n3. (b) Express P(k). { (k-1)!(n-k)! } Here, the ordering does not matter. \newcommand{\imp}{\rightarrow} (1!)(1!)(2!)] 3 0 obj << Discrete Math Cheat Sheet by Dois via cheatography.com/11428/cs/1340/ Complex Numbers j = -1 j = -j j = 1 z = a + bj z = r(sin + jsin) z = re tan b/a = A cos a/r Above Venn Diagram shows that A is a subset of B. We say that $\{A_i\}$ is a partition if we have: Remark: for any event $B$ in the sample space, we have $\displaystyle P(B)=\sum_{i=1}^nP(B|A_i)P(A_i)$. Number of permutations of n distinct elements taking n elements at a time = $n_{P_n} = n!$, The number of permutations of n dissimilar elements taking r elements at a time, when x particular things always occupy definite places = $n-x_{p_{r-x}}$, The number of permutations of n dissimilar elements when r specified things always come together is $r! /ProcSet [ /PDF /Text ] on April 20, 2023, 5:30 PM EDT. Types of propositions based on Truth values1.Tautology A proposition which is always true, is called a tautology.2.Contradiction A proposition which is always false, is called a contradiction.3.Contingency A proposition that is neither a tautology nor a contradiction is called a contingency. DISCRETE MATHEMATICS FOR COMPUTER SCIENCE - Duke No. Variance The variance of a random variable, often noted Var$(X)$ or $\sigma^2$, is a measure of the spread of its distribution function. endobj /ImageMask true Now we want to count large collections of things quickly and precisely. If there are n elements of which $a_1$ are alike of some kind, $a_2$ are alike of another kind; $a_3$ are alike of third kind and so on and $a_r$ are of $r^{th}$ kind, where $(a_1 + a_2 + a_r) = n$. ~C'ZOdA3,3FHaD%B,e@,*/x}9Scv\`{]SL*|)B(u9V|My\4 Xm$qg3~Fq&M?D'Clk +&$.U;n8FHCfQd!gzMv94NU'M`cU6{@zxG,,?F,}I+52XbQN0.''f>:Vn(g."]^{\p5,`"zI%nO. %PDF-1.5 [/Pattern /DeviceRGB] %PDF-1.4 )$. WebTrig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 p < /Type /ExtGState There are n number of ways to fill up the first place. \newcommand{\R}{\mathbb R} \newcommand{\twoline}[2]{\begin{pmatrix}#1 \\ #2 \end{pmatrix}} 2 0 obj << Cram sheet/Cheat sheet/study sheet for a discrete math class that covers sequences, recursive formulas, summation, logic, sets, power sets, functions, combinatorics, arrays and matrices. Did you make this project? Share it with us! I Made It! I go out of my way to simplify subjects. The remaining 3 vacant places will be filled up by 3 vowels in $^3P_{3} = 3! Combinatorics 71 5.3. From a set S ={x, y, z} by taking two at a time, all permutations are , We have to form a permutation of three digit numbers from a set of numbers $S = \lbrace 1, 2, 3 \rbrace$. The number of all combinations of n things, taken r at a time is , $$^nC_{ { r } } = \frac { n! } Let s = q + r and s = e f be written in lowest terms. \newcommand{\Q}{\mathbb Q} Bipartite Graph : There is no edges between any two vertices of same partition . Cumulative distribution function (CDF) The cumulative distribution function $F$, which is monotonically non-decreasing and is such that $\underset{x\rightarrow-\infty}{\textrm{lim}}F(x)=0$ and $\underset{x\rightarrow+\infty}{\textrm{lim}}F(x)=1$, is defined as: Remark: we have $P(a < X\leqslant B)=F(b)-F(a)$.

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