In a chess tournament 16 members played in tournament x and 20 played in…
2023
In a chess tournament 16 members played in tournament x and 20 played in tournament y and 12 in both the tournaments , if each player played atleast one of these tournaments , what is the total number of players ?
- A.
48
- B.
36
- C.
32
- D.
24
Attempted by 30 students.
Show answer & explanation
Correct answer: D
Answer: 24
Use the inclusion–exclusion principle to count the total number of distinct players.
Let X be the set of players in tournament X (16 players) and Y be the set of players in tournament Y (20 players).
Formula: total = |X ∪ Y| = |X| + |Y| − |X ∩ Y|
Compute: 16 + 20 − 12 = 24
Explanation: Adding 16 and 20 counts the 12 players who played both tournaments twice, so we subtract that overlap once to get the correct total of distinct players.