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

Three cards are drawn at random from a pack of $52$ cards. What is the chance of drawing three aces

There are $3$ bags $A, B$ & $C$. Bag $A$ contains $1$ Red & $2$ Green balls, bag $B$ contains $2$ Red & $1$ Green balls and bag $C$ contains only one green ball. One ball is drawn from bag $A$ & put into bag $B$ then one ball is drawn from $B$ & put into bag $C$ & finally one ball is drawn from bag $C$ & put into bag $A$. When this operation is completed, probability that bag $A$ contains $2$ Red & $1$ Green balls, is -

Let $X$ be a set containing $10$ elements and $P(X)$ be its power set. If $A$ and $B$ are picked up at random from $P(X),$ with replacement, then the probability that $A$ and $B$ have equal number elements, is

A card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a square is

The probability of hitting a target by three marks men is $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu$ then $\lambda + \mu$ is equal to :-