In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play

An alternate approach -- one that does not require advance knowledge of a formula -- is to GUEES AND CHECK.

7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and Football.
Meaning:
7 students play AT LEAST H AND C
4 students play AT LEAST C AND F
5 students play AT LEAST H AND F

Case 1: 1 student plays all 3 sports
Subtracting this 1 student from each of the three groups above, we get:
Number who play only H and C = (number who play at least H and C) - (number who play all 3) = 7-1 = 6
Number who play only C and F = (number who play at least C and F) - (number who play all 3) = 4-1 = 3
Number who play only H and F = (number who play at least H and F) - (number who play all 3) = 5-1 = 4
Adding together the resulting values, we get:
Number who play exactly two sports = 6+3+4 = 13
Since 13 is not among the answer choices, Case 1 is not viable.

Case 2: 2 students play all 3 sports
Subtracting these 2 students from each of the three groups above, we get:
Number who play only H and C = (number who play at least H and C) - (number who play all 3) = 7-2 = 5
Number who play only C and F = (number who play at least C and F) - (number who play all 3) = 4-2 = 2
Number who play only H and F = (number who play at least H and F) - (number who play all 3) = 5-2 = 3
Adding together the resulting values, we get:
Number who play exactly two sports = 5+2+3 = 10
Since 10 is among the answer choices, Case 2 is viable.

If the number who play all 3 sports INCREASES, the number who play exactly two sports will DECREASE below 10.
Since no answer choice is less than 10, only Case 2 is viable, implying that the number who play exactly two sports = 10