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 24 頁
... result of part a to evaluate the sum m n ( 1 ) ( m ) n k + ( 1 ) ( x 2 ) + ( 2 ) ( ( 2 ) ( x x m ― 2 ) 2 ) n + + ( m ) . Remark . For other methods of determining this sum , see the solutions to problems 571 , 60a , 61c . 73a . Banach's ...
... result of part a to evaluate the sum m n ( 1 ) ( m ) n k + ( 1 ) ( x 2 ) + ( 2 ) ( ( 2 ) ( x x m ― 2 ) 2 ) n + + ( m ) . Remark . For other methods of determining this sum , see the solutions to problems 571 , 60a , 61c . 73a . Banach's ...
第 140 頁
... result it follows in particular that the numbers of people who arrive at the three leftmost crossings B1 , B2 , and B , are respectively ( 1000 ) = 1 , ( 1000 ) = 1000 , and ( 1000 ) = ( 1000 · 999 ) / 2 = 499,500 . 2 This same result ...
... result it follows in particular that the numbers of people who arrive at the three leftmost crossings B1 , B2 , and B , are respectively ( 1000 ) = 1 , ( 1000 ) = 1000 , and ( 1000 ) = ( 1000 · 999 ) / 2 = 499,500 . 2 This same result ...
第 230 頁
... result of problem 83a , the answer to problem 54 is obtained immediately from this , Inasmuch as the answer to problem 53b can be derived from the answer to problem 54 ( compare with the solution to problem 54 ) , the reasoning ...
... result of problem 83a , the answer to problem 54 is obtained immediately from this , Inasmuch as the answer to problem 53b can be derived from the answer to problem 54 ( compare with the solution to problem 54 ) , the reasoning ...
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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