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

If $7$ identical white balls and $3$ identical black balls are arranged in a row at random,what is the probability that no two black balls are together?

$A$ 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 $3$ red,$7$ white and $4$ black balls. If three balls are drawn from the bag,then the probability that all of them are of the same colour is

Two numbers are selected at random from the numbers $1, 2, \dots, n$. The probability that the difference between the first and second number is not less than $m$ (where $0 < m < n$) is

$A$ bag contains $a$ white and $b$ black balls. Two players $A$ and $B$ alternately draw a ball from the bag,replacing the ball each time after the draw,until one of them draws a white ball and wins the game. $A$ begins the game. If the probability of $A$ winning the game is three times that of $B$,then the ratio $a : b$ is