A dice is rolled three times, find the probability of getting a larger number than the previous number each time ?

A box $'A'$ contanis $2$ white, $3$ red and $2$ black balls. Another box $'B'$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $'B'$ is

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

Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1,2,3,4,5$ and $6$ are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$ is

A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is

If six students, including two particular students $A$ and $B,$ stand in a row, then the probability that $A$ and $B$ are separated with one student in between them is