Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively?

$A$ bag contains $12$ two-rupee coins,$7$ one-rupee coins,and $4$ fifty-paise coins. If three coins are selected at random,the probability that the sum of the values of the three coins is not an integral multiple of a rupee is:

The probability of getting a king and a spade card when two cards are drawn simultaneously from a pack of $52$ playing cards is

Two different families $A$ and $B$ are blessed with an equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of family $B$ is $\frac{1}{12}$,then the number of children in each family is?

From a group of $50$ students,two sections comprising of $20$ and $30$ students are formed. If $Ram$ and $Rahim$ are two particular students among the $50$ students,then the probability that they both belong to the same section is

There are $10$ bulbs in a room,out of which $4$ are defective. If $3$ bulbs are chosen at random,what is the probability that the room will be illuminated? (The room is illuminated if at least one bulb is good.)