Find the probability that the birth days of six different persons will fall in exactly two calendar months.

Explanation

Since anyone's birthday can fall in one of 12 months, so total number of ways is `12^(6)`.
Now, any two months can be chosen in `.^(12)C_(2)` ways. The six birthdays can fall in these two months in `2^(6)` ways. Out of these `2^(6)` ways there are two ways when all the six birthdays fall in one month. So, favorable number of ways is `.^(12)C_(2) xx (2^(6) - 2)`. Hence, required probability is
`(.^(12)C_(2)xx(2^(6)-2))/(12^(6))=(12xx11xx(2^(5-1)))/(12^(6)) = (341)/(12^(5))`