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 9 筆
第 26 頁
... letters and sealed them in envelopes without writing the addresses on the envelopes . Having forgot- ten which letter he had put into which envelope , he wrote the n addresses on the envelopes at random . What is the probability that at ...
... letters and sealed them in envelopes without writing the addresses on the envelopes . Having forgot- ten which letter he had put into which envelope , he wrote the n addresses on the envelopes at random . What is the probability that at ...
第 166 頁
... letter ( say , A and a ) are next to each other can be determined in the following way . Arrange the 18 slips bearing the letters other than A and a in a circle in any way such that capital letters alternate with small letters ; this ...
... letter ( say , A and a ) are next to each other can be determined in the following way . Arrange the 18 slips bearing the letters other than A and a in a circle in any way such that capital letters alternate with small letters ; this ...
第 168 頁
... letter , we proceed as follows . Arrange the 10 capital letters in a circle ; as was shown above , this can be done in 9 ! essentially different ways . The 10 small letters can then be placed next to the corresponding capital letters in ...
... letter , we proceed as follows . Arrange the 10 capital letters in a circle ; as was shown above , this can be done in 9 ! essentially different ways . The 10 small letters can then be placed next to the corresponding capital letters in ...
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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