Twenty persons arrive in a town having $3$ hotels $x, y$ and $z$. If each person randomly chooses one of these hotels,then what is the probability that at least $2$ of them go to hotel $x$,at least $1$ to hotel $y$,and at least $1$ to hotel $z$? (Each hotel has a capacity for more than $20$ guests.)

The sum of all the elements in the set $\{n \in \{1, 2, \ldots, 100\} \mid \text{H.C.F. of } n \text{ and } 2040 \text{ is } 1\}$ is equal to $.....$

There are exactly twelve Sundays in the period from January $1$ to March $31$ in a certain year. Then,the day corresponding to February $15$ in that year is

$A$ group of $40$ students appeared in an examination of $3$ subjects - Mathematics,Physics,and Chemistry. It was found that all students passed in at least one of the subjects. $20$ students passed in Mathematics,$25$ students passed in Physics,and $16$ students passed in Chemistry. At most $11$ students passed in both Mathematics and Physics,at most $15$ students passed in both Physics and Chemistry,and at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students who passed in all the three subjects is . . . . . . .

In a class of $35$ students,$24$ like to play cricket and $16$ like to play football. Also,each student likes to play at least one of the two games. How many students like to play both cricket and football?

In a city,$25\%$ of families have a telephone and $15\%$ have a car,while $65\%$ of families have neither a telephone nor a car. If $2000$ families have both a car and a telephone,then consider the following statements:
$1.$ $10\%$ of families have both a car and a telephone.
$2.$ $35\%$ of families have either a car or a telephone.
$3.$ $40,000$ families live in the city.
Which of these statements are true?