If $n(X)=700, n(A)=200, n(B)=300,$ and $n(A \cap B)=100$,where $X$ is the universal set and $A$ and $B$ are subsets of $X$,then $n(A' \cap B')=$

The probabilities that a student passes in Mathematics,Physics,and Chemistry are $m, p$,and $c$ respectively. The student has a $75\%$ chance of passing in at least one,a $50\%$ chance of passing in at least two,and a $40\%$ chance of passing in exactly two. Which of the following relations are true?

Let $A$ be a set containing $n$ elements. If $P$ and $Q$ are two subsets of $A$, then the number of ways of choosing $P$ and $Q$ such that $P \cap Q = \phi$ is:

Let $A = \{n \in [100, 700] \cap \mathbb{N} : n \text{ is neither a multiple of } 3 \text{ nor a multiple of } 4\}$. Then the number of elements in $A$ is

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$, $B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then, the correct order of their probabilities is:

Of the members of three athletic teams in a school,$21$ are in the cricket team,$26$ are in the hockey team,and $29$ are in the football team. Among them,$14$ play hockey and cricket,$15$ play hockey and football,and $12$ play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is: