Three mangoes and three apples are in a box. If two fruits are chosen at random, the probability that one is a mango and the other is an apple is

There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, is a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Two digits are selected randomly from the set $\{1, 2,3, 4, 5, 6, 7, 8\}$ without replacement one by one. The probability that minimum of the two digits is less 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 $x _3 < x _4 < x _5 ?$

A bag contains $4$ white, $5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is