Question

11. In a class of 60 students, 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. Find
() How many play hockey, basketball and cricket
(ii) How many play hockey but not cricket
How many play hockey and cricket but not basketball​

Answer 1

Step-by-step explanation:

Let B, C and H be the sets of students that plays Basketball, Cricket and Hockey

n(H) = 23, n(B) = 15, n(C) = 20

n(H intersection B) = 7, n(C intersection B) = 5, n(H intersection C) = 4

n(H union B union C) = 60 – 15 = 45

1. Hence, students that plays all games,

n(H intersection B intersection C) = n(H union B union C) – n(H) – n(B) – n(C) + n(H intersection B) + n(B intersection C) + n(C intersection H)

= 45 – 23 – 15 – 20 + 7 + 5 + 4 = 3

2. Who plays hockey not cricket

n(H) – n(H intersection C) = 23 – 4 = 19

3. Plays cricket and hockey not basketball

n(H intersection C) – n(H intersection C intersection B)

4 -3 = 1