A bag contains $6$ white, $7$ red and $5$ black balls. If $3$ balls are drawn from the bag at random, then the probability that all of them are white is
$\frac{{20}}{{204}}$
$\frac{5}{{204}}$
$\frac{1}{3}$
None of these
If six students, including two particular students $A$ and $B,$ stand in a row, then the probability that $A$ and $B$ are separated with one student in between them is
In a lottery there were $90$ tickets numbered $1$ to $90$. Five tickets were drawn at random. The probability that two of the tickets drawn numbers $15$ and $89$ is
Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to
If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are
A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is :