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Question 1
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The coefficient of $x^{50}$ in the expression of ${(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001x^{1000}}$
A.
$${}^{1005}{{C}}_{50}$$
B.
$${}^{1005}{{C}}_{48}$$
C.
$${}^{1002}{{C}}_{50}$$
D.
$${}^{1002}{{C}}_{51}$$
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