Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
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第 1 到 3 筆結果,共 12 筆
第 54 頁
... inclusion and exclusion , — # ( AU BUC ) = 199 + 142 + 333 28 66 47 +9 ―― = 542 . The elements AUBUC are the positive integers ≤ 999 which are divisible by either 5 or 7 or 3. Since we want to know how many integers in this range are ...
... inclusion and exclusion , — # ( AU BUC ) = 199 + 142 + 333 28 66 47 +9 ―― = 542 . The elements AUBUC are the positive integers ≤ 999 which are divisible by either 5 or 7 or 3. Since we want to know how many integers in this range are ...
第 75 頁
... inclusion and exclusion to compute # ( A ) and # ( B ) . = Let A , be the set of all partitions of n in which the integer rk occurs as one of the parts . Then A A1 U A2 U A , U. , where there are actually only a finite number of non ...
... inclusion and exclusion to compute # ( A ) and # ( B ) . = Let A , be the set of all partitions of n in which the integer rk occurs as one of the parts . Then A A1 U A2 U A , U. , where there are actually only a finite number of non ...
第 159 頁
... inclusion and exclusion ( see problem 12 ) . Let A , be the set of all outcomes in which the first letter is correctly addressed , A , the set of outcomes where the second letter is correctly addressed , etc. Then A1 U A2 U U Am is the ...
... inclusion and exclusion ( see problem 12 ) . Let A , be the set of all outcomes in which the first letter is correctly addressed , A , the set of outcomes where the second letter is correctly addressed , etc. Then A1 U A2 U U Am is the ...
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A₁ A₂ An+m arrangements b₁ b₂ binomial coefficients binomial theorem bishops black squares chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain P₁ pairs partition passengers plane polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks S₁ segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices