The coefficient of $ x^{7} $ in the expression $ (1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+\ldots+x^{10} $ is [JEE Main 2020, 7 Jan (Shift 2)]

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The coefficient of \( x^{7} \) in the expression \( (1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+\ldots+x^{10} \) is [JEE Main 2…