There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is
$\frac{1}{{5\,!}}$
$\frac{{50\,!}}{{55\,!}}$
$\frac{1}{{{{50}^5}}}$
None of these
A bag contains $4$ white, $5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is
Two dice are thrown $5$ times, and each time the sum of the numbers obtained being $5$ is considered a success. If the probability of having at least $4$ successes is $\frac{\mathrm{k}}{3^{11}}$, then $\mathrm{k}$ is equal to
An ordinary cube has four blank faces, one face marked $2$ another marked $3$. Then the probability of obtaining a total of exactly $12$ in $5$ throws, is
A card is drawn from a pack of $52$ playing cards. The card is replaced and pack is shuffled. If this is done six times, then the probability that $2$ hearts, $2$ diamond and $2$ black cards are drawn is
If two different numbers are taken from the set $\left\{ {0,1,2,3, \ldots ,10} \right\}$, then the probability that their sum as well as absolute difference are both multiple of $4$, is