From a well shuffled pack of $52$ playing cards, cards are drawn one by one with replacement. Probability that $5^{th}$ card will be "king of hearts" is
$\frac{{{{51}^4}}}{{{{52}^5}}} \times 5{C_1} \times 4!$
$\frac{{{{51}^4}}}{{{{52}^5}}} \times 4!$
$\frac{{{{51}^4}}}{{{{52}^5}}}$
$\frac{{{{51}^5}}}{{{{52}^5}}}$
Twenty tickets are marked the numbers $1, 2, ..... 20.$ If three tickets be drawn at random, then what is the probability that those marked $7$ and $11$ are among them
The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system $\mathrm{A}\left[\begin{array}{l}\mathrm{x} \\ \mathrm{y} \\ \mathrm{z}\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is
Two numbers $x$ and $y$ are chosen at random from the set of integers $\{1,2,3,4......15\}.$ The probability that point $(x,y)$ lies on a line through $(0,0)$ having slope $\frac{2}{3}$ is
A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:
Five digit numbers are formed using the digits $1, 2, 3, 4, 5, 6$ and $8$. What is the probability that they have even digits at both the ends