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 seven digit number is formed using digits $3 ,3,4,4,4,5,5 .$ The probability, that number so formed is divisible by $2,$ is ..... .

There are $n$ different objects $1, 2, 3,......n$ distributed at random in $n$ places marked $1, 2, 3, ......n$. The probability that at least three of the objects occupy places corresponding to their number is

A card is drawn from a pack of $52$ playing cards. The card is replaced and pack is  shuffled. If this is done six times, then the probability that $2$ hearts, $2$ diamond and $2$ black cards are drawn is

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$, is

A box contains coupons labelled $1,2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x _3 < x _4 < x _5 ?$