The candidate has to select at least 2 questions from each group. So, he can select 2 questions from group
A,2 questions from group
B and 3 questions from group
C, or 2 questions from group
A,3 questions from group
B and 2 questions from group
C, or 3 questions from group
A,2 questions from group
B and 2 questions from group
C. These are the only possible combinations.
Let's calculate the number of ways to choose each of these combinations:
2 from
A,2 from
B,3 from
C :
The number of ways to choose 2 questions from group A is
‌4C2=‌=6. The number of ways to choose 2 questions from group B is
‌5C2=‌=10. The number of ways to choose 3 questions from group C is
‌6C3=‌=20. So, the total number of ways to choose this combination is
6*10*20=1200.
2 from
A,3 from
B,2 from
C :
The number of ways to choose 2 questions from group A is
‌4C2=6.
The number of ways to choose 3 questions from group B is
‌5C3=‌=10.
The number of ways to choose 2 questions from group C is
‌6C2=‌=15.
So, the total number of ways to choose this combination is
6*10*15=900.
3 from
A,2 from
B,2 from
C :
The number of ways to choose 3 questions from group A is
‌4C3=‌=4.
The number of ways to choose 2 questions from group B is
‌5C2=10.
The number of ways to choose 2 questions from group C is
‌6C2=15.
So, the total number of ways to choose this combination is
4*10*15=600.
Therefore, the total number of ways the candidate can make his selection is
1200+900+600= 2700 .
So the answer is Option C.