A five digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetitions. Then the probability that the number is divisible by $4$ is

Two friends $A$ and $B$ have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to daughters of $A$ is $1/20$. The number of daughters each of them have is

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

Let a computer program generate only the digits $0$ and $1$ to form a string of binary numbers with probability of occurrence of $0$ at even places be $\frac{1}{2}$ and probability of occurrence of $0$ at the odd place be $\frac{1}{3}$. Then the probability that $'10'$ is followed by $'01'$ is equal to :

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

Fifteen persons among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$, is