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…

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