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 43 筆
第 103 頁
... drawn in the plane ; let us draw the ( k + 1 ) st line and see by how much it increases the number of pieces into which the plane is divided . The ( k + 1 ) st line meets each of the k lines which have already been drawn ; the k points ...
... drawn in the plane ; let us draw the ( k + 1 ) st line and see by how much it increases the number of pieces into which the plane is divided . The ( k + 1 ) st line meets each of the k lines which have already been drawn ; the k points ...
第 156 頁
... draw any of = 2 2 2n 2 second person can draw any of the = ( 2n - 2 2 ) ( 2n 3 ) / 2 pairs which can be formed from the remaining 2n2 balls . The third can draw any of to - last person , - ( 2n 2 4 ) = ( 2n - 4 ) ( 2n - 5 ) / 2 pairs ...
... draw any of = 2 2 2n 2 second person can draw any of the = ( 2n - 2 2 ) ( 2n 3 ) / 2 pairs which can be formed from the remaining 2n2 balls . The third can draw any of to - last person , - ( 2n 2 4 ) = ( 2n - 4 ) ( 2n - 5 ) / 2 pairs ...
第 158 頁
... draw one white ball and one black ball . Hence we have only to consider the case of even n = 2k ; the total number ... draw a pair of white balls ( and consequently , the other k each draw a pair of black balls ) . The k people can each ...
... draw one white ball and one black ball . Hence we have only to consider the case of even n = 2k ; the total number ... draw a pair of white balls ( and consequently , the other k each draw a pair of black balls ) . The k people can each ...
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常見字詞
A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares C₁ 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 G₁ 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 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