Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ .

Solution

$C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096 $

$\therefore 2^n = 4096 =2^{12} $

$\Rightarrow n = 12 $

Greatest coefficient = ${}^{12}{C_6} = 924$