In a certain town $25\%$ families own a phone and $15\%$ own a car, $65\%$ families own neither a phone nor a car. $2000$ families own both a car and a phone. Consider the following statements in this regard:

$1$. $10\%$ families own both a car and a phone

$2$. $35\%$ families own either a car or a phone

$3$. $40,000$ families live in the town

Which of the above statements are correct

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 class of $140$ students numbered $1$ to $140$, all even numbered students opted Mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is

A group of $40$ students appeared in an examination of $3$ subjects – Mathematics, Physics  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, $16$ students passed in Chemistry, at most $11$ students passed in both Mathematics and Physics, at most $15$ students passed in both Physics and Chemistry, at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is___________.

In a class of $100$ students,$15$ students chose only physics (but not mathematics and chemistry),$3$ chose only chemistry (but not mathematics and physics), and $45$ chose only mathematics(but not physics and chemistry). Of the remaining students, it is found that $23$ have taken physics and chemistry,$20$ have taken physics and mathematics, and $12$ have taken mathematics and chemistry. The number of student who chose all the three subjects is