Two coins are tossed. Find the probability that two heads are obtained.

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

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

From a group of $7$ men and $4$ ladies,a committee of $6$ persons is formed. What is the probability that the committee contains exactly $2$ ladies?

$A$ bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. $A$ bag and a ball out of it are picked at random. The probability that the ball is white,is

$A$ bag contains $8$ black and $7$ white balls. Two balls are drawn at random. For which of the following is the probability the highest?