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 group of $10$ men and $5$ women,a four-member committee is to be formed such that it must contain at least one woman. The probability that the committee has more women than men is:

If $3$ numbers are chosen from the first $15$ natural numbers,what is the probability that the numbers are in arithmetic progression?

There are $6$ positive and $8$ negative numbers. If four numbers are chosen at random and multiplied,the probability that the product is a negative number is

Consider the set of all $7$-digit numbers formed by the digits $0, 1, 2, 3, 4, 5, 6$,each chosen exactly once. If a number is randomly drawn from this set,the probability that it is divisible by $4$ 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