32 students play basketball and 25 students play volleyball. It is found that 20 students playb0th the games. Find the number of students playing at least one game. Also, find total number ofstudents if 13 students play none of these games
Question
32 students play basketball and 25 students play volleyball. It is found that 20 students playb0th the games. Find the number of students playing at least one game. Also, find total number ofstudents if 13 students play none of these games
Solution
To solve this problem, we can use the principle of inclusion and exclusion.
Step 1: First, we add the number of students who play basketball and volleyball. 32 (basketball players) + 25 (volleyball players) = 57 students
Step 2: However, we have double-counted the students who play both games. So, we subtract the number of students who play both games. 57 (from step 1) - 20 (students who play both games) = 37 students
So, there are 37 students who play at least one game.
To find the total number of students, we add the number of students who play at least one game to the number of students who don't play any game.
37 (students who play at least one game) + 13 (students who play none of these games) = 50 students
So, the total number of students is 50.
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