Q. 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 $100\, k$, then $k$ is equal to_______.
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