A bag contains $20$ coins. If the probability that bag contains exactly $4$ biased coin is $1/3$ and that of exactly $5$ biased coin is $2/3$,then the probability that all the biased coin are sorted out from the bag in exactly $10$ draws is
$\frac{5}{{33}}\frac{{{}^{16}{C_6}}}{{{}^{20}{C_9}}} + \frac{1}{{11}}\frac{{{}^{15}{C_5}}}{{{}^{20}{C_9}}}$
$\frac{2}{{33}}\left( {\frac{{2.{}^{16}{C_6} + 5{}^{15}{C_5}}}{{{}^{20}{C_9}}}} \right)$
$\frac{2}{{33}}\frac{{{}^{16}{C_7}}}{{{}^{20}{C_9}}} + \frac{1}{{11}}\frac{{{}^{15}{C_6}}}{{{}^{20}{C_9}}}$
none of these
Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q- p$ is equal to
A bag contains $3$ red, $4$ white and $5$ blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is
Word ‘$UNIVERSITY$’ is arranged randomly. Then the probability that both ‘$I$’ does not come together, is
From eighty cards numbered $1$ to $80$, two cards are selected randomly. The probability that both the cards have the numbers divisible by $4$ is given by
If four persons are chosen at random from a group of $3$ men, $2$ women and $4 $ children. Then the probability that exactly two of them are children, is