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 44 筆
第 50 頁
... compute how many of the integers under consideration do not have any I's among their digits . By adjoining O and deleting 10,000,000,000 , we obtain a sequence of 1010 numbers in which there is one more number with no 1's among its ...
... compute how many of the integers under consideration do not have any I's among their digits . By adjoining O and deleting 10,000,000,000 , we obtain a sequence of 1010 numbers in which there is one more number with no 1's among its ...
第 159 頁
... compute the number of favorable outcomes , i.e. outcomes where at least one envelope is correctly addressed . ... We will do this by applying the principle of inclusion and exclusion ( see problem 12 ) . Let A , be the set of all ...
... compute the number of favorable outcomes , i.e. outcomes where at least one envelope is correctly addressed . ... We will do this by applying the principle of inclusion and exclusion ( see problem 12 ) . Let A , be the set of all ...
第 203 頁
... compute the number ƒ ( N ) of favorable outcomes , i.e. , outcomes in which a and b are relatively prime . To do this we will first compute the number g ( N ) of unfavorable outcomes ; then f ( N ) = N2 − g ( N ) . Let P1 , P2 ...
... compute the number ƒ ( N ) of favorable outcomes , i.e. , outcomes in which a and b are relatively prime . To do this we will first compute the number g ( N ) of unfavorable outcomes ; then f ( N ) = N2 − g ( N ) . Let P1 , P2 ...
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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