$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is
$5/126$
$1/126$
$4/126$
$6/125$
A box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession then the probability that one is red and other is green, 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)
A mapping is selected at random from the set of all the mappings of the set $A = \left\{ {1,\,\,2,\,...,\,n} \right\}$ into itself. The probability that the mapping selected is an injection is
A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is