In a sports event attended by 50 people 24 played football and 28 played cricket, some played both football and cricket. Find the number of people who played both football and cricket
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To find the number of people who played both football and cricket, we can use a method called the inclusion-exclusion principle.
Step 1: Find the number of people who played football only.
Since 24 people played football and some played both football and cricket, we need to subtract the number of people who played both from the total number of football players.
Football-only players = Total football players - Number of people who played both football and cricket.
Step 2: Find the number of people who played cricket only.
Similarly, since 28 people played cricket and some played both football and cricket, we need to subtract the number of people who played both from the total number of cricket players.
Cricket-only players = Total cricket players - Number of people who played both football and cricket.
Step 3: Find the number of people who played both football and cricket.
To find this, we can use the inclusion-exclusion principle:
Number of people who played both football and cricket = Total football players + Total cricket players - Total number of people.
Now, let's calculate the values using the given information:
Total football players = 24
Total cricket players = 28
Total number of people = 50
Using the above formula, we can compute the number of people who played both football and cricket:
Number of people who played both football and cricket = 24 + 28 - 50
Number of people who played both football and cricket = 52 - 50
Number of people who played both football and cricket = 2
Therefore, the number of people who played both football and cricket is 2.