Ok,
Let's first make all combination and then solve each combination and add all to get the final result
All the cases which involves atleast one science and atlease one art , and total subject choosen have to be four :
Science Art Other Total
C( 4 , 1 ) * C( 3 , 1 ) * C( 3 , 2 ) 36
C( 4 , 1 ) * C( 3 , 2 ) * C( 3 , 1 ) 36
C( 4 , 1 ) * C( 3 , 3 ) * C( 3 , 0 ) 4
C( 4 , 2 ) * C( 3 , 1 ) * C( 3 , 1 ) 54
C( 4 , 2 ) * C( 3 , 2 ) * C( 3 , 0 ) 18
C( 4 , 3 ) * C( 3 , 1 ) * C( 3 , 0 ) 12
Total ways : 36 + 36 + 4 + 54 + 18 + 12 : 160 ways
So, anwer will be (D) option
We don't multiply the answer to 4! because classes are same, (Science1 , Art1 , Other1 , Other2 ) and
(Science1 , Other1 , Art1 , Other2 ) both are same, hence not counted as different.