The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :

In four schools ${B_1},{B_2},{B_3},{B_4}$ the percentage of girls students is $12, 20, 13, 17$ respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is ${B_2},$ is

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

A mapping is selected at random from the set of all the mappings of the set $A = \left\{ {1,\,\,2,\,...,\,n} \right\}$ into itself. The probability that the mapping selected is an injection is

Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that you both enter the same section ?

The probability, that in a randomly selected $3-$digit number at least two digits are odd, is