$A$ college awarded $38$ medals in football,$15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports,how many received medals in exactly two of the three sports?

$A$ and $B$ are two subsets of set $S = \{1, 2, 3, 4\}$ such that $A \cup B = S$. Then,the number of ordered pairs $(A, B)$ is:

$205$ students take an examination,of whom $105$ pass in English,$70$ students pass in Mathematics,and $30$ students pass in both. How many students fail in both subjects?

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 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?