Question

In a group of 50 students, the number of students like playing hockey, cricket and football were found to be as: cricket 17 hockey 15, football 13, football and hockey 4, hockey and cricket 5, cricket and football 9 and 3 students play all three sports. Find no. of students who play (1) cricket only (2) football and hockey but not cricket (3) at least one of all three sports (4) none of the three sports

Answer 1

Answer:

Step-by-step explanation:

n(C) = 17, n(H) = 15, n(F) = 13

n(FnH) = 4, n(HnC) = 5 , n(CnF) = 9,

n(CnFnH) = 3

1. n(Cricket only) = n(C) - n(CnF) - n(CnH) + n(CnFnH) = 17 - 9 - 5 + 3 = 6.

2. n(FnHnC') = n(FnH) - n(FnHnC) = 4 - 3 = 1.

3. n(CuHuF) = n(C) + n(F) + n(H) - n(CnF) - n(CnH) - n(FnH) + n(CnFnH)

                    = 17 + 13 + 15 - 9 - 5 - 4 + 3 = 30

4. None of the 3 games = 50 - 30 = 20.

Answer 2

Answer:

Venn Diagram

Step-by-step explanation:

First write all the given details..