$A$ and $B$ are non-singleton sets and $n(A \times B) = 35$. If $B \subset A$,then ${}^{n(A)}C_{n(B)}$ is equal to

There is a group of $265$ persons who like either singing,dancing,or painting. In this group,$200$ like singing,$110$ like dancing,and $55$ like painting. If $60$ persons like both singing and dancing,$30$ like both singing and painting,and $10$ like all three activities,then the number of persons who like only dancing and painting is:

Let $S = \{4, 6, 9\}$ and $T = \{9, 10, 11, \ldots, 1000\}$. If $A = \{a_{1} + a_{2} + \ldots + a_{k} : k \in N, a_{1}, a_{2}, \ldots, a_{k} \in S\}$,then the sum of all the elements in the set $T - A$ is equal to:

In a certain school,$74 \%$ of students like cricket,$76 \%$ of students like football,and $82 \%$ of students like tennis. Then,all three sports are liked by at least $...... \%$ of students.

The probability that at least one of the events $E_1$ and $E_2$ occurs is $0.6$. If the probability of the simultaneous occurrence of $E_1$ and $E_2$ is $0.2$,then $P(E_1') + P(E_2') = $

In a school,there are $21$ students in the cricket team,$26$ in the hockey team,and $29$ in the football team. Among these,$14$ play both hockey and cricket,$15$ play both hockey and football,and $12$ play both football and cricket. If $8$ students play all three games,find the total number of students in the three athletic teams.