Official solution
(1 + x)10 + x(1 + x)9
+ x2(1 + x)8
+ ......+ x10
This is a G.P where
First term, a = (1 + x)10
common ratio, r = \[{x \over {1 + x}}\]
Number of terms = 11
Sum of G.P
= \[{{{{\left( {1 + x} \right)}^{10}}\left( {1 - {{\left( {{x \over {1 + x}}} \right)}^{11}}} \right)} \over {1 - {x \over {1 + x}}}}\]
= (1 + x)11
-- x11
So Coefficient of x7
is 11C7 = 330