If the papers of $4$ students can be checked by any one of $7$ teachers,then the probability that all the $4$ papers are checked by exactly $2$ teachers is (in $/49$)

If a person throws $3$ dice,what is the probability that the sum of the numbers obtained is exactly $15$?

If $4$ cards are drawn one by one from a deck of $52$ cards,what is the probability that each card belongs to a different suit?

If $6$ boys and $3$ girls are to be seated on $9$ chairs for a photograph,then the probability that the end seats are occupied by the girls and no two girls are side by side is

Ten persons with badges numbered $1$ to $10$ are in a room. If three of them are asked to leave the room, then the probability that the person with the smallest badge number among the three who left is $5$, 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