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 34 頁
... remark below ) . In the following problems , however , such doubt can scarcely arise : in all of them it is possible to define " at random " in almost the same way as in the above examples , and this is the way the term is to be ...
... remark below ) . In the following problems , however , such doubt can scarcely arise : in all of them it is possible to define " at random " in almost the same way as in the above examples , and this is the way the term is to be ...
第 49 頁
... Remark . ( 16 ) = € 8008 . If there are n different flavors available and the number of ice cream cones to be selected is m , then the number of ways of choosing them is m + n n - 1 こり' ) = ( ' m + n - m -1 ) . This can be proved in ...
... Remark . ( 16 ) = € 8008 . If there are n different flavors available and the number of ice cream cones to be selected is m , then the number of ways of choosing them is m + n n - 1 こり' ) = ( ' m + n - m -1 ) . This can be proved in ...
第 56 頁
... Remark . As in the remark to problem 13 , the principle of inclusion and exclusion for m sets can be applied to prove the following generalization of the result just obtained : If N is a positive integer , and N = P11P2Pmm is its ...
... Remark . As in the remark to problem 13 , the principle of inclusion and exclusion for m sets can be applied to prove the following generalization of the result just obtained : If N is a positive integer , and N = P11P2Pmm is its ...
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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 given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number multiple 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