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 unit digit of k is equal to_____

There are 5 students in class 10, 6 students in class 11 and 8 students in class 12.
Number of ways, in which 10 students can be selected, according to given conditions 
10th class          11th class             12th class
2                                 2                                    6           $\Rightarrow 5_{C_2}\times 6_{C_2}\times 8_{C_6}$         
2                                 3                                    5            $\Rightarrow 5_{C_2}\times 6_{C3}\times 8_{C5}$            
3                                 2                                    5          $\Rightarrow 5_{C_3}\times 6_{C2}\times 8_{C5}$                  
$\therefore$ total number of ways  $=5_{C_2}\times 6_{C_2}\times 8_{C_6}+5_{C_2}\times 6_{C_3}\times 8_{C_5}+5_{C_3}\times 6_{{ }_{C_2}}\times 8_{C_2}=23800$
But total number of ways = 100k [given] $\Rightarrow 100k=23800\Rightarrow k=238$