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Find the number of ways in which the birthday of six different persons will fall in exactly two calendar months.

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Correct Answer - `.^(12)C_(2)xx(2^(6)-2)`
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, the required number of ways is `.^(12)C_(2)xx(2^(6)-2)`.

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