$A$ bag contains $12$ pairs of socks. If $4$ socks are picked up at random,the probability that there is at least one pair is equal to

In a shoe rack,there are $4$ pairs of shoes. If $4$ shoes are drawn one after the other at random without replacement,what is the probability of getting at least one correct pair of shoes among the four shoes drawn?

$A$ bag contains $6$ white and $4$ black balls. $A$ die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white 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

The numbers $2, 3, 5, 7, 11, 13$ are written on six distinct paper chits. If $3$ of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by $3$ is:

Let $A$ denote the event that a $6$-digit integer formed by $0, 1, 2, 3, 4, 5, 6$ without repetitions is divisible by $3$. Then the probability of event $A$ is equal to: