Given that in a class of 50 students, 20 play Hockey, 15 play Cricket, and 11 play Football, with 18 students not playing any sport, how many students play exactly two of these sports?

To determine how many students play exactly two sports, it is essential to analyze the distribution of the students among the different sports and those who do not participate in any sport.

Initially, there are 50 students in the class, out of which 18 do not play any sport. This means 32 students participate in at least one sport (50 total students - 18 not playing any sports).

Now, consider the number of students playing each sport:

• 20 students play Hockey

• 15 students play Cricket

• 11 students play Football

To find how many students play exactly two sports, we can use a bit of logical deduction and the principle of inclusion-exclusion.

Let:

• H represent the number of students who play Hockey,

• C represent the number of students who play Cricket,

• F represent the number of students who play Football,

• x represent the students who play all three sports.

Using the principle of inclusion-exclusion, we can write the equation for the total number of unique students playing:

Total = (H + C + F) - (students playing exactly two sports) - 2x

From the data provided:

Total = 32 (number of students playing at least one sport)

H + C