If a $5$-digit number is chosen at random,what is the probability that all digits are distinct,odd digits occupy odd places,and even digits occupy even places?

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:

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 a well-shuffled deck of $52$ cards,$13$ cards are selected at random. The probability that the selected $13$ cards contain exactly $4$ kings is ....

$A$ bag contains $5$ red balls,$3$ black balls,and $4$ white balls. Three balls are drawn at random. The probability that they are not of the same colour is

$A$ mapping is selected at random from the set of all the mappings of the set $A = \{1, 2, ..., n\}$ into itself. The probability that the mapping selected is an injection is