In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exact : Crackverbal Support

In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many stud Print

Modified on: Tue, 12 Oct, 2021 at 4:03 PM

Concept: The question tests the advanced understanding on Overlapping sets.

Solution:

Let Hockey = H ; Football= F ; Cricket = C

We know Total = H +C+ F - [(H∩C) + (C∩H) + (H∩F)] + (H∩C∩F) + Neither

=> 50 = 20+15+11 -[ 7+4+5 ] + (H∩C∩F) + 18

=> H∩C∩F = 2

Exactly two of these sports = Only HC + Only HC + Only HF

Number of students playing ONLY Hockey and Cricket

= (H∩C)-(H∩C∩F ) = 7 - 2 = 5

Number of students playing ONLY Cricket and Football

= (C∩F) - (H∩C∩F )= 4-2 = 2

Number of students playing ONLY Hockey and Football

= (H∩F) - (H∩C∩F ) = 5-2 = 3

Thus, number of students play exactly two of these sports. = 5+2+3=10 (Option B)

Did you find it helpful? Yes No

In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many stud Print

Related Articles