Let \( \bigcup_{i=1}^{50} X_{i}=\bigcup_{i=1}^{n} Y_{i}=T \), where each \( X_{i} \) contains \(10\) elements and each \…

Let \( \bigcup_{i=1}^{50} X_{i}=\bigcup_{i=1}^{n} Y_{i}=T \), where each \( X_{i} \) contains \(10\) elements and each \( Y_{i} \) contains \(5\) elements. If each element of the set \( T \) is an element of exactly \(20\) of sets \( X_{i}'s \) and exactly 6 of sets \( Y_{i}'s \) then \( n \) is equal to

[JEE Main 2020, 4 Sep (Shift 2)]