$A$ bag contains $4$ white,$5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white,a red and a green ball is drawn is

Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.$ $A$ mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection is

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains all $4$ Kings.

From the first $100$ natural numbers, two numbers $a$ and $b$ are selected randomly without replacement. If the probability that $a-b \ge 10$ is $\frac{m}{n}$, with $\gcd(m, n)=1$, then $m+n$ is equal to:

Two numbers are selected at random from the numbers $1, 2, \dots, n$. The probability that the difference between the first and second number is not less than $m$ (where $0 < m < n$) is

If $6$ boys and $3$ girls are to be seated on $9$ chairs for a photograph,then the probability that the end seats are occupied by the girls and no two girls are side by side is