If $f(y) = 1 - (y - 1) + {(y - 1)^2} - {(y - 1)^{^3}} + ... - {(y - 1)^{17}},$ then the coefficient of $y^2$ in it is

  • [AIEEE 2012]
  • A

    $^{17}{C_2}$

  • B

    $^{17}{C_3}$

  • C

    $^{18}{C_2}$

  • D

    $^{18}{C_3}$

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