Question:
If the sum of the coefficients in the expansion of $(x+y)^{n}$ is 4096 , then the greatest coefficient in the expansion is
Solution:
$(x+y)^{n} \Rightarrow 2^{n}=4096 \quad 2^{10}=1024 \times 2$
$\Rightarrow 2^{n}=2^{12} \quad 2^{11}=2048$
$\mathrm{n}=12 \quad 2^{12}=\underline{4096}$
${ }^{12} C_{6}=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2 \times 1}$
$=11 \times 3 \times 4 \times 7$
$=924$
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