From a group of $10$ men and $5$ women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is

A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed $3$ times, then the probability of getting two tails and one head is-

Three squares of a chess board are chosen at random, the probability that two are of one colour and one of another is

Two numbers are selected at random from $1, 2, 3 ......100$ and are multiplied, then the probability correct to two places of decimals that the product thus obtained is divisible by $3$, 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 $x _3 < x _4 < x _5 ?$

From eighty cards numbered $1$ to $80$, two cards are selected randomly. The probability that both the cards have the numbers divisible by $4$ is given by