From $3n$ consecutive integers, three integers are selected at random. The probability that their sum is divisible by $3$ is

If $3$ dice are thrown, the probability of getting $10$ as the sum of the three numbers that appeared on the top faces of the dice is

There are $10$ engineering colleges and five students $A, B, C, D, E$. Each of these students received an offer from all of these $10$ engineering colleges. They randomly choose a college independently of each other. The probability that all get admission in different colleges can be expressed as $\frac{a}{b}$,where $a$ and $b$ are co-prime numbers. Then the value of $a + b$ is:

If two numbers $a$ and $b$ are chosen from the first $30$ natural numbers,what is the probability that $a^2 - b^2$ is divisible by $3$?

$A$ committee of $5$ is to be formed from a group of $9$ people. What is the probability that a specific married couple is either both included or both excluded from the committee?

Two friends $A$ and $B$ have an equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to the daughters of $A$ is $1/20$. The number of daughters each of them has is: