The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :
$\frac{65}{2^{7}}$
$\frac{65}{2^{8}}$
$\frac{135}{2^{9}}$
$\frac{35}{2^{7}}$
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
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
A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is :
Four boys and three girls stand in a queue for an interview, probability that they will in alternate position is
Twenty persons arrive in a town having $3$ hotels $x, y$ and $z$. If each person randomly chooses one of these hotels, then what is the probability that atleast $2$ of them goes in hotel $x$, atleast $1$ in hotel $y$ and atleast $1$ in hotel $z$ ? (each hotel has capacity for more than $20$ guests)