In a class of $60$ students,$25$ students play cricket and $20$ students play tennis,and $10$ students play both the games. The number of students who play neither is:

In a group of $65$ people,$40$ like cricket and $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

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

If $S$ and $T$ are two sets such that $S$ has $21$ elements,$T$ has $32$ elements,and $S \cap T$ has $11$ elements,how many elements does $S \cup T$ have?

In a committee of $25$ members,each member is proficient either in Mathematics or in Statistics or in both. If $19$ of them are proficient in Mathematics and $16$ of them are proficient in Statistics,then the probability that a person selected at random from the committee is proficient in both is

Let $S = \{1, 2, 3, 5, 7, 10, 11\}$. The number of nonempty subsets of $S$ such that the sum of all elements is a multiple of $3$ is $........$