Question

In a class of 60 stutents of XI, 23 play hockey, 15 play basketball, 20 play cricket and 7 play hockey and basketball, 5 play cricket and basketball, 4 play hockey and cricket, 15 do not play any of the three games. 1x5=5 Choose the correct alternatives using the above information. 1. How many students play hockey, basketball and cricket together? (a) 3 (b) 4 (c) 2 (d) 1 2. How many students play hockey but not cricket? (a) 16 (b) 15 (c) 19 (d) 10 3. How many students play hockey and cricket but not basketball ? (a) 3 (b) 4 (c)2 (d) 1 4. How many students play cricket but not hockey? (b) 18 (c) 20 (a) 16 (d) 11 5. How many students play hockey and basketball but not cricket? (c) 3 (b) 4 D (a) 7 (d) 2​

Answer 1

Answer:

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Answer 2

Given :  In a class of 60 students of XI,

23 play hockey, 15 play basketball, 20 play cricket and 7 play hockey and basketball, 5 play cricket and basketball, 4 play hockey and cricket, 15 do not play any of the three games.  

To Find :  1. Students play hockey, basketball and cricket  together

2. Students play hockey but not cricket

3. Students play hockey and cricket but not basketball

4. Students play cricket but not hockey

5. Students play hockey and basketball but not cricket

Solution:

n ( Total) = 60

n(H) = 23

n (B) = 15

n(C) = 20

n ( H ∩ B) = 7

n ( H ∩ C) = 4

n ( C ∩ B) = 5

n ( H ∩ B ∩ C ) = ?

n (none) = 15

n ( Total) = n(H)  + n (B)  + n(C) - n ( H ∩ B) - n ( H ∩ C)  - n ( C ∩ B) + n ( H ∩ B ∩ C )  + n (none)

=> 60 = 23 + 15 + 20 - 7 - 4 - 5 +  n ( H ∩ B ∩ C ) + 15

=>  n ( H ∩ B ∩ C ) = 3

Students play hockey, basketball and cricket  together = n ( H ∩ B ∩ C ) = 3

Students play hockey but not cricket  

= n(H) -  n ( H ∩ C)

= 23 - 4

= 19

Students play hockey and cricket but not basketball  

= n ( H ∩ C)  -  n ( H ∩ B ∩ C )  

= 4 - 3

= 1

Students play cricket but not hockey  

= n(C) - n ( H ∩ C)

= 20 - 4

= 16

Students play hockey and basketball but not cricket

=  n ( H ∩ B)  -  n ( H ∩ B ∩ C )  

= 7 - 3

= 4

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