Let ∪ i = 1 50 X i = ∪ i = 1 n Y i = T , where each X i contains 10 elements and each Y i…

Let $\underset{i=1}{\overset{50}{\cup }}{X}_i=\underset{i=1}{\overset{n}{\cup }}{Y}_i=T$, 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 :