If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member. What is the probability that you will be on the committee
$\left( \begin{array}{l}38\\\,3\end{array} \right)$
$\left( \begin{array}{l}37\\\,2\end{array} \right)$
$\frac{{\left( \begin{array}{l}37\\{\rm{ }}2\end{array} \right)}}{{\left( \begin{array}{l}38\\{\rm{ }}3\end{array} \right)}}$.
$\frac{{666}}{{8436}}$
In a box, there are $20$ cards, out of which $10$ are lebelled as $\mathrm{A}$ and the remaining $10$ are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A-$card is obtained. The probability that the second $A-$card appears before the third $B-$card is
In four schools ${B_1},{B_2},{B_3},{B_4}$ the percentage of girls students is $12, 20, 13, 17$ respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is ${B_2},$ is
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
In an examination, there are $10$ true-false type questions. Out of $10$ , a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k }{4^{10}}$, then $k$ is equal to