In a room of 36 people, 20 players play chess while 28 players play poker. How many players play both?

Question: In a room of 36 people, 20 players play chess while 28 players play poker. How many players play both?

Solution:
Given that,
Total number of people in the room = 36.
Number of people who play chess = 20.
Number of people who play poker = 28.
We need to find the number of people who play both chess and poker.

We know that,
∣C ∪ P∣ = ∣C∣ + ∣P∣ - ∣C ∩ P∣
⇒ 36 = 20 + 28 - ∣C ∩ P∣
⇒ 36 = 48 - ∣C ∩ P∣
⇒ ∣C ∩ P∣ = 48 - 36
∴ ∣C ∩ P∣ = 12