Suppose A<sub>1</sub>, A<sub>2</sub>, A<sub>3</sub>, ..., A<sub>30</sub> are thirty sets each having 5 elements with no common elements across the sets and B<sub>1</sub>, B<sub>2</sub>, ..., B<sub>n</sub> are n sets each with 3 elements with no common elements across the sets. Let <span class="math-tex">\(\rm \displaystyle\bigcup^{30}_{i = 1} A_i = \displaystyle\bigcup^n_{j = 1} B_j = S\)</span> and each elements of S belongs to exactly 10 of the A<sub>i</sub>'s and exactly 9 of the B<sub>j</sub>'s. Then n is equal to
Count total memberships two ways.
Answer: (D) 45
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