From a class of $12$ girls and $18$ boys, two students are chosen randomly. What is the probability that both of them are girls

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to

A five digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetitions. Then the probability that the number is divisible by $4$ is

Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q- p$ is equal to

A binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is