Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that ${a^2} - {b^2}$ is divisible by $3$ is

  • A

    $\frac{9}{{87}}$

  • B

    $\frac{{12}}{{87}}$

  • C

    $\frac{{15}}{{87}}$

  • D

    $\frac{{47}}{{87}}$

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  • [JEE MAIN 2013]