$3$ letters are placed randomly into $3$ envelopes. What is the probability that exactly one letter is placed in the correct envelope?

$A$ bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is

$A$ bag contains $5$ blue and an unknown number $x$ of red balls. Two balls are drawn at random. If the probability of both of them being blue is $\frac{5}{14}$,then the value of $x$ is equal to

Two distinct numbers $a$ and $b$ are selected at random from ${1, 2, 3, \dots, 50}$. The probability that their product $ab$ is divisible by $3$ is:

$A$ bag contains $6$ red,$5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red,is

$A$ class has $15$ boys and $5$ girls. Suppose $3$ students are selected at random from the class. The probability that there are $2$ boys and $1$ girl is