In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?
Practice Questions
1 question
Q1
In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?
22
20
15
10
Using inclusion-exclusion, the number of students who play either sport is: (Cricket + Football - Both) = 12 + 15 - 5 = 22.
Questions & Step-by-step Solutions
1 item
Q
Q: In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?
Solution: Using inclusion-exclusion, the number of students who play either sport is: (Cricket + Football - Both) = 12 + 15 - 5 = 22.
Steps: 6
Step 1: Identify the number of students who play cricket. This is 12 students.
Step 2: Identify the number of students who play football. This is 15 students.
Step 3: Identify the number of students who play both cricket and football. This is 5 students.
Step 4: Use the inclusion-exclusion principle to find the total number of students who play either cricket or football. The formula is: (Number of cricket players) + (Number of football players) - (Number of students who play both).
Step 5: Plug in the numbers: 12 (cricket) + 15 (football) - 5 (both) = 22.
Step 6: The final answer is that 22 students play either cricket or football.
