Question

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 $100k$, then $k$ is equal to

Answer 1

5 6 8
10th 11th 12th
$(2,2,6):\Rightarrow 10\times 15\times 28=4200$
$(2,3,5):\Rightarrow 10\times 20\times 56=11200$
$(3,2,5):\Rightarrow 10\times 15\times 56=8400$
$\therefore 23800=100k$