Three squares of a chessboard are chosen at random. The probability that two are of one colour and one is of another colour is:

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw a sum of $9$ with both dice will be awarded the prize. If $A$ throws first,then the probability that $B$ wins the game 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:

In a game of cards,what is the probability that a specific player holds all $4$ kings in a hand of $13$ cards?

$A$ company representative is distributing $5$ identical samples of a product among $12$ houses in a row such that each house gets at most one sample. The probability that no two consecutive houses get one sample is

$A$ bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour is