# Let's Unite Them!

Let us say $$A_1,A_2,A_3,\ldots ,A_{30}$$ are thirty sets containing 6 elements each. While $$B_1,B_2,B_3,\ldots ,B_n$$ are $$n$$ sets containing 3 elements each. Now consider the following;

$\large\displaystyle \mathop{\bigcup}_{k=1}^{30}A_k=\mu=\displaystyle \mathop{\bigcup}_{k=1}^{n}B_k$

Such that, each element of $$\mu$$ belongs to exactly 10 elements of $$A_k$$'s and exactly 9 elements of $$B_k$$'s, then find the value of $$n$$.

Notation: The symbol $$\cup$$ denotes set union, and $\large\displaystyle\mathop{\bigcup}_{k=1}^{m}X_k=X_1\cup X_2\cup X_3\cup\dots\cup X_m.$

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