In a class of $55$ students,$23$ study Mathematics,$24$ study Physics,$19$ study Chemistry,$12$ study Mathematics and Physics,$9$ study Mathematics and Chemistry,$7$ study Physics and Chemistry,and $4$ study all three subjects. Find the number of students who study exactly one subject.

$A$ market research group conducted a survey of $1000$ consumers and reported that $720$ consumers like product $A$ and $450$ consumers like product $B$. What is the least number of consumers that must have liked both products?

In a survey of $220$ students of a higher secondary school,it was found that at least $125$ and at most $130$ students studied Mathematics; at least $85$ and at most $95$ studied Physics; at least $75$ and at most $90$ studied Chemistry; $30$ studied both Physics and Chemistry; $50$ studied both Chemistry and Mathematics; $40$ studied both Mathematics and Physics and $10$ studied none of these subjects. Let $m$ and $n$ respectively be the least and the most number of students who studied all the three subjects. Then $m+n$ is equal to .............................

The number of $3$-digit numbers that are divisible by either $3$ or $4$ but not divisible by $48$ is:

The probability of failing in Physics is $20\%$,and the probability of failing in Mathematics is $10\%$. What is the probability of failing in at least one subject (in $\%$)?

The number of $3$-digit numbers that are divisible by either $2$ or $3$ but not divisible by $7$ is $.........$.