There are $5$ students in class $10,6$ students in class $11$ and $8$ students in class $12.$ If the number of ways, in which $10$ students can be selected from them so as to include at least $2$ students from each class and at most $5$ students from the total $11$ students of class $10$ and $11$ is $100 \mathrm{k}$, then $\mathrm{k}$ is equal to $......$

  • [JEE MAIN 2021]
  • A

    $240$

  • B

    $245$

  • C

    $270$

  • D

    $238$

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