Three integers are chosen at random from the first $20$ integers. The probability that their product is even, is
$\frac{2}{{19}}$
$\frac{3}{{29}}$
$\frac{{17}}{{19}}$
$\frac{4}{{19}}$
There are $n$ different objects $1, 2, 3,......n$ distributed at random in $n$ places marked $1, 2, 3, ......n$. The probability that at least three of the objects occupy places corresponding to their number is
A mapping is selected at random from the set of all the mappings of the set $A = \left\{ {1,\,\,2,\,...,\,n} \right\}$ into itself. The probability that the mapping selected is an injection is
Word ‘$UNIVERSITY$’ is arranged randomly. Then the probability that both ‘$I$’ does not come together, is
If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is
A lot consists of $12$ good pencils, $6$ with minor defects and $2$ with major defects. A pencil is choosen at random. The probability that this pencil is not defective is