The coefficient of $x^{50}$ in the binomial expansion of ${\left( {1 + x} \right)^{1000}} + x{\left( {1 + x} \right)^{999}} + {x^2}{\left( {1 + x} \right)^{998}} + ..... + {x^{1000}}$ is
The coefficient of $x^{50}$ in the binomial expansion of ${\left( {1 + x} \right)^{1000}} + x{\left( {1 + x} \right)^{999}} + {x^2}{\left( {1 + x} \right)^{998}} + ..... + {x^{1000}}$ is
- [JEE MAIN 2014]
- A
$\frac{{\left( {1000} \right)!}}{{\left( {50} \right)!\left( {950} \right)!}}$
- B
$\frac{{\left( {1000} \right)!}}{{\left( {49} \right)!\left( {951} \right)!}}$
- C
$\frac{{\left( {1001} \right)!}}{{\left( {51} \right)!\left( {950} \right)!}}$
- D
$\frac{{\left( {1001} \right)!}}{{\left( {50} \right)!\left( {951} \right)!}}$
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