$$ \begin{aligned} & A=\{1,2,3,4\} ; P(A)=\frac{3}{4} \rightarrow \text { Correct } \\ & B=\{5,6,7,8,9,10\} ; P(B)=\frac{1}{4} \text { Correct } \end{aligned} $$ 8 Correct Ans.: $$ \begin{aligned} & (4,4):{ }^4 \mathrm{C}_4\left(\frac{3}{4}\right)^4 \cdot{ }^6 \mathrm{C}_4 \cdot\left(\frac{1}{4}\right)^4 \cdot\left(\frac{3}{4}\right)^2 \\ & (3,5):{ }^4 \mathrm{C}_3\left(\frac{3}{4}\right)^3 \cdot\left(\frac{1}{4}\right)^1 \cdot{ }^6 \mathrm{C}_5\left(\frac{1}{4}\right)^5 \cdot\left(\frac{3}{4}\right) \\ & (2,6):{ }^4 \mathrm{C}_2\left(\frac{3}{4}\right)^2\left(\frac{1}{4}\right)^2 \cdot{ }^6 \mathrm{C}_6\left(\frac{1}{4}\right)^6 \\ & \text { Total }=\frac{1}{4^{10}}\left[3^4 \times 15 \times 3^2+4 \times 3^3 \times 6 \times 3+6 \times 3^2\right] \\ & =\frac{27}{4^{10}}[2.7 \times 15+72+2] \\ & \Rightarrow \mathrm{K}=479 \end{aligned} $$