If the value of the definite integral \( \int_{0}^{1}{ }^{207} C_{7} x^{200} \cdot(1-x)^{7} d x ...

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If the value of the definite integral \( \int_{0}^{1}{ }^{207} C_{7} x^{200} \cdot(1-x)^{7} d x \) is equal to \( \frac{1}{k} \) where \( k \in N \). The value of ' \( k \) ' is equal to :
(a) 208
(b) 210
(c) 212
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