Let _i=1^50 X_i=_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…

Let $\displaystyle \bigcup_{i=1}^{50} \mathrm{X}_i=\bigcup_{i=1}^{\mathrm{n}} \mathrm{Y}_i=\mathrm{T}$, where each $\displaystyle \mathrm{X}_i$ contains $\displaystyle 10$ elements and each $\displaystyle \mathrm{Y}_i$ contains $\displaystyle 5$ elements. If each element of the set T is an element of exactly $\displaystyle 20$ of sets $\displaystyle X_i{ }^{\prime}$ s and exactly $\displaystyle 6$ of sets $\displaystyle Y_i^{\prime}$ s, then n is equal to :