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 146 頁
... passengers can choose which cars to sit in is 3 · 3 = 32. Similarly , the number of ways nine passengers can choose which cars to sit in is 39. There are therefore 3o equally likely possible outcomes . Let us now determine the number of ...
... passengers can choose which cars to sit in is 3 · 3 = 32. Similarly , the number of ways nine passengers can choose which cars to sit in is 39. There are therefore 3o equally likely possible outcomes . Let us now determine the number of ...
第 162 頁
... passengers choosing at random ( independently of the others ) one of the m carriages of the train . One passenger has m possibilities for the choice of his carriage , two passengers have m2 possibilities , . . . , and p passengers have ...
... passengers choosing at random ( independently of the others ) one of the m carriages of the train . One passenger has m possibilities for the choice of his carriage , two passengers have m2 possibilities , . . . , and p passengers have ...
第 163 頁
... passengers can be put into them so that none is empty in ( 6 ) - ( 1 ) α- - 1 ) 1 ) " + ( 2 ) αr – 2 ) P - ... + ... passengers can be arranged in m carriages so that exactly r carriages are occupied ( we consider the number m to be ...
... passengers can be put into them so that none is empty in ( 6 ) - ( 1 ) α- - 1 ) 1 ) " + ( 2 ) αr – 2 ) P - ... + ... passengers can be arranged in m carriages so that exactly r carriages are occupied ( we consider the number m to be ...
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常見字詞
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