If A = left{ begin{bmatrix} a_1 & b_1 & c_1 | vedclass

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(B) The binomial coefficients in the expansion of $(1+x)^{11}$ are given by $^{11}C_r$ for $r = 0, 1, 2, \dots, 11$.These are: $^{11}C_0, ^{11}C_1, ^{

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$6$

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(B) The binomial coefficients in the expansion of $(1+x)^{11}$ are given by $^{11}C_r$ for $r = 0, 1, 2, \dots, 11$.These are: $^{11}C_0, ^{11}C_1, ^{11}C_2, ^{11}C_3, ^{11}C_4, ^{11}C_5, ^{11}C_6, ^{11}C_7, ^{11}C_8, ^{11}C_9, ^{11}C_{10}, ^{11}C_{11}$.Using the property $^{n}C_r = ^{n}C_{n-r}$,we have:$^{11}C_0 = ^{11}C_{11}, ^{11}C_1 = ^{11}C_{10}, ^{11}C_2 = ^{11}C_9, ^{11}C_3 = ^{11}C_8, ^{11}C_4 = ^{11}C_7, ^{11}C_5 = ^{11}C_6$.Thus,there are $6$ distinct values for the binomial coefficients.Each of the $9$ entries $(a_1, b_1, c_1, a_2, b_2, c_2, a_3, b_3, c_3)$ in the $3 	imes 3$ matrix can be any of these $6$ distinct values.Therefore,the total number of elements in set $A$ is $6^9$.

If $A = \left\{ \begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{bmatrix} : a_i, b_i, c_i \in \{ \text{binomial coefficients in the expansion of } (1+x)^{11} \} \right\}$,then the number of elements in set $A$ is: (in $^9$)

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