There are \(5\) students in class \(10,6\) students in class \(11\) and \(8\) students in class \(12\). If the number of…

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 \( k \) is equal to

[JEE Main 2021, 25 Jul (Shift 1)]