A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll, $i=2,3$, is equal to :

If three letters can be posted to any one of the $5$ different addresses, then the probability that the three letters are posted to exactly two addresses is:

A debate club consists of $6$ girls and $4$ boys. A team of $4$ members is to be selected from this club including the selection of a captain (from among these $4$ memiers) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

Three vertices are chosen randomly from the seven vertices of a regular $7$ -sided polygon. The probability that they form the vertices of an isosceles triangle is

Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1,2,3,4,5$ and $6$ are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$ is