If a number is chosen at random from the first $200$ positive integers,what is the probability that it is divisible by $6$ or $8$?

$A$ 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?

$A$ group of $40$ students appeared in an examination of $3$ subjects - Mathematics,Physics,and Chemistry. It was found that all students passed in at least one of the subjects. $20$ students passed in Mathematics,$25$ students passed in Physics,and $16$ students passed in Chemistry. At most $11$ students passed in both Mathematics and Physics,at most $15$ students passed in both Physics and Chemistry,and at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students who passed in all the three subjects is . . . . . . .

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{3, 6, 7, 9\}$. Then the number of elements in the set $\{ C \subseteq A : C \cap B \neq \phi \}$ is

$A$ survey shows that $73 \%$ of the persons working in an office like coffee,whereas $65 \%$ like tea. If $x$ denotes the percentage of them who like both coffee and tea,then $x$ cannot be

$A$ number is selected at random from the set $\{1, 2, 3, 4, \ldots, 1000\}$. What is the probability of getting a number which is a perfect cube or a natural number having an odd number of divisors?