Total number of question =11
Part 1 contains5 questions and part 2 contain 6 questions.
A student has to select 6 questions all in which there is at least 2 questions from each part.
Now different possibilities can occur.
Part1 (5 questions) Part2 (6 questions)
3 3
4 2
2 4
Now total number of ways is
= (5C3 × 6C3 )+ ( 5C4 × 6C2 ) + ( 5C2× 6C4 )$
= {(5×4×6×5)/ (2×3×2)+ {(5×6 ×5)/(2)} + {(5×4×6 ×5)/(2×2)}$
= 200 + 75 + 150
= 425
So, the total number of ways a student can select the questions is 425
Note: We have to take at least3 questions at once, not in different parts like first take3, then2, etc.
If we do so, then it is wrong because it is given in the question that we have to take at least 2 questions at once.