Let A_1, A_2, dots, A_{11} be players in a te | vedclass

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(D) Let $x_i$ be the number of coins given to player $A_i$. The total number of coins is $\sum_{i=1}^{11} x_i = 100$.Given conditions: $x_i \ge i+1$ f

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$^{27}C_{10}$

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(D) Let $x_i$ be the number of coins given to player $A_i$. The total number of coins is $\sum_{i=1}^{11} x_i = 100$.Given conditions: $x_i \ge i+1$ for $i=3, 4, \dots, 11$,$x_1 \ge 1+5=6$,and $x_2 \ge 2+3=5$.Let $y_i = x_i - (i+1)$ for $i=3, \dots, 11$,$y_1 = x_1 - 6$,and $y_2 = x_2 - 5$.Substituting these into the sum: $(y_1+6) + (y_2+5) + \sum_{i=3}^{11} (y_i + i + 1) = 100$.$y_1 + y_2 + \dots + y_{11} + 11 + \sum_{i=1}^{11} i = 100$.$y_1 + y_2 + \dots + y_{11} + 11 + \frac{11 	imes 12}{2} = 100$.$y_1 + y_2 + \dots + y_{11} + 11 + 66 = 100$.$y_1 + y_2 + \dots + y_{11} = 100 - 77 = 23$.Wait,re-evaluating the base distribution: $x_1 \ge 6, x_2 \ge 5, x_3 \ge 4, x_4 \ge 5, \dots, x_{11} \ge 12$.Sum of minimums $= 6+5+4+5+6+7+8+9+10+11+12 = 83$.Remaining coins $= 100 - 83 = 17$.Using stars and bars,the number of ways to distribute $17$ coins among $11$ players is $^{17+11-1}C_{11-1} = ^{27}C_{10}$.

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