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 13 筆
第 172 頁
... bills as there are with ten - dollar bills ahead of that point . Let q ( n , m ) be the probability of the event B that at each point of the line ( including the end ) there are more customers with five - dollar bills than there are ...
... bills as there are with ten - dollar bills ahead of that point . Let q ( n , m ) be the probability of the event B that at each point of the line ( including the end ) there are more customers with five - dollar bills than there are ...
第 178 頁
... bills as with three - dollar bills ahead of that point . To each such arrangement of customers there corresponds a " staircase " A04142 An + m whose base A , will not lie in the shade when the staircase is illuminated from above by a ...
... bills as with three - dollar bills ahead of that point . To each such arrangement of customers there corresponds a " staircase " A04142 An + m whose base A , will not lie in the shade when the staircase is illuminated from above by a ...
第 179 頁
... bills and m who have only three - dollar bills ( a total of n + m people ) , and the second consisting of n + 1 customers with one - dollar bills and m with only three - dollar bills ( a total of n + m + 1 people ) . Then the ...
... bills and m who have only three - dollar bills ( a total of n + m people ) , and the second consisting of n + 1 customers with one - dollar bills and m with only three - dollar bills ( a total of n + m + 1 people ) . Then the ...
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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