In a class, 12 students play cricket, 15 play football, and 5 play both. How man

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Question: In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?

Options:

Correct Answer: 22

Solution:

Using inclusion-exclusion, the number of students who play either sport is: (Cricket + Football - Both) = 12 + 15 - 5 = 22.

In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?

In a class, 12 students play cricket, 15 play football, and 5 play both. How many students play either cricket or football?

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.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of multiple sets by including the sizes of the individual sets and excluding the sizes of their intersections.