Out of $800$ boys in a school,$224$ played cricket,$240$ played hockey,and $336$ played basketball. Of the total,$64$ played both basketball and hockey,$80$ played cricket and basketball,and $40$ played cricket and hockey. $24$ played all three games. The number of boys who did not play any game is:

If ${A_1}, {A_2}, {A_3}, \dots, {A_{30}}$ are $30$ sets each having $5$ elements and ${B_1}, {B_2}, \dots, {B_n}$ are $n$ sets each having $3$ elements. Let $\bigcup_{i=1}^{30} {A_i} = \bigcup_{j=1}^n {B_j} = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s,then $n$ is equal to:

In a certain town, $60 \%$ of the families own a car, $30 \%$ own a house and $20 \%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?

Consider a three-digit number $N = 100x + 10y + z$,where $x, y, z$ are the digits at the hundreds,tens,and units places respectively. The number satisfies the following properties:
$I$. If its digits in the units place and tens place are interchanged,the number increases by $36$.
$II$. If its digits in the units place and hundreds place are interchanged,the number decreases by $198$.
If the digits in the tens place and hundreds place are interchanged,then the number:

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

The smallest set $A$ such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$ is