Let $S = \{(a, b) : a, b \in \mathbb{Z}, 0 \leq a, b \leq 18\}$. The number of elements $(x, y)$ in $S$ such that $3x + 4y + 5$ is divisible by $19$ is:

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam,$60 \%$ of the total candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. $A$ candidate is randomly chosen from the qualified candidates. The probability that the chosen candidate is a female is:

$A$ and $B$ are two subsets of set $S = \{1, 2, 3, 4\}$ such that $A \cup B = S$. Then,the number of ordered pairs $(A, B)$ is:

In a survey of $60$ people,it was found that $25$ people read newspaper $H$,$26$ read newspaper $T$,$26$ read newspaper $I$,$9$ read both $H$ and $I$,$11$ read both $H$ and $T$,$8$ read both $T$ and $I$,and $3$ read all three newspapers. Find the number of people who read at least one of the newspapers.

There are $200$ individuals with a skin disorder,$120$ had been exposed to the chemical $C_{1}$,$50$ to chemical $C_{2}$,and $30$ to both the chemicals $C_{1}$ and $C_{2}$. Find the number of individuals exposed to chemical $C_{2}$ but not chemical $C_{1}$.

In a city of $10,000$ families,$40\%$ families buy newspaper $A$,$20\%$ buy newspaper $B$,$10\%$ buy newspaper $C$,$5\%$ buy newspapers $A$ and $B$,$3\%$ buy $B$ and $C$,and $4\%$ buy $A$ and $C$. If $2\%$ families buy all three newspapers,find the number of families that buy only newspaper $A$.