+2440 Solution:
One method for visualizing a solution is to view the cards in a 4 X 4 matrix, where the columns represent the players and the rows represent the cards in the players' hands. Valid conditions for success occur when the players have single “A” cards located in any one of the four positions of their respective hands.
\(\left[ {\begin{array}{cccc} A & A & A & A \\ X & X & X & X \\ X & X & X & X \\ X & X & X & X \\ \end{array} } \right] \text {First arrangement of “A} \scriptsize{s} \normalsize \text {" where“X” is any other card}\\ \left[ {\begin{array}{cccc} A & A & A & X \\ X & X & X & A \\ X & X & X & X \\ X & X & X & X \\ \end{array} } \right] \text {Second arrangement} \\ \left[ {\begin{array}{cccc} A & A & X & A \\ X & X & A & X \\ X & X & X & X \\ X & X & X & X \\ \end{array} } \right] \text {Fifth arrangement} \\ \left[ {\begin{array}{cccc} X & X & X & X \\ X & X & X & X \\ X & X & X & X \\ A & A & A & A \\ \end{array} } \right] \text {Last arrangement} \)
From this, it’s easy to see there are (4^4) = 256 arrangements of success.
Dividing the number of successes by the total number of combinations
(44) / (nCr(16,4)), gives (64/445) ≈ 0.1406593.
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Here are two other solution methods for this question:
https://web2.0calc.com/questions/probability-help_11#r5
Here, Melody presents the total arrangements without the target cards then adds the arrangements of the target cards.
https://web2.0calc.com/questions/probability-help_11#r13
Here, Rom presents the arrangements of each hand without the target cards then adds the arrangements of the target cards to each hand in sequence.
GA
