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 62 筆
第 21 頁
... example we might wish to know the probability that an even number will turn up when a die is thrown . In this case the given set of outcomes consists of 2 , 4 , and 6 . Such a set E is called an event ; if the outcome of the experiment ...
... example we might wish to know the probability that an even number will turn up when a die is thrown . In this case the given set of outcomes consists of 2 , 4 , and 6 . Such a set E is called an event ; if the outcome of the experiment ...
第 48 頁
... example , F1F1FFFF , would mean a choice of 2 ice cream cones of flavor F1 , one of F , etc. Now let us draw vertical lines to separate the F's from the F's , the F's from the F3's , ... , and finally the F10's from the F11's . In the ...
... example , F1F1FFFF , would mean a choice of 2 ice cream cones of flavor F1 , one of F , etc. Now let us draw vertical lines to separate the F's from the F's , the F's from the F3's , ... , and finally the F10's from the F11's . In the ...
第 174 頁
... example , in fig . 62b , n = 7 , m = 4 , and exactly 7 4 3 of the points are illuminated . We have thus proved that for n > m exactly n m of the n + m arrangements of customers obtained from any one arrangement by successively putting ...
... example , in fig . 62b , n = 7 , m = 4 , and exactly 7 4 3 of the points are illuminated . We have thus proved that for n > m exactly n m of the n + m arrangements of customers obtained from any one arrangement by successively putting ...
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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