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 8 筆
第 148 頁
... balls . Since k balls can be selected from the ( n + m n + m in k different ways , there are ' n k + m ) equally likely possible outcomes to our experiment . The favorable ones are those in which exactly r of the k balls drawn are white ...
... balls . Since k balls can be selected from the ( n + m n + m in k different ways , there are ' n k + m ) equally likely possible outcomes to our experiment . The favorable ones are those in which exactly r of the k balls drawn are white ...
第 157 頁
... balls with ( 2n 2 ) corresponding possible outcomes for the drawing of the second pair , then combining each of the ( 2n ) ( 22 ) possibilities 2 ( 2n 4 ) possible 2 thus obtained for the first two pairs of balls with the outcomes for ...
... balls with ( 2n 2 ) corresponding possible outcomes for the drawing of the second pair , then combining each of the ( 2n ) ( 22 ) possibilities 2 ( 2n 4 ) possible 2 thus obtained for the first two pairs of balls with the outcomes for ...
第 158 頁
... balls is odd , at least one of the people must draw one white ball and one black ball . Hence we have only to ... balls ( and consequently , the other k each draw a pair of black balls ) . The k people can each draw a pair of white balls ...
... balls is odd , at least one of the people must draw one white ball and one black ball . Hence we have only to ... balls ( and consequently , the other k each draw a pair of black balls ) . The k people can each draw a pair of white balls ...
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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