Probability of Birthdays in Two Months

Total possible distributions of 4 birthdays across 12 months = $12^4$. Number of ways to choose 2 months = $\binom{12}{2} = 66$. For each chosen pair of months, each person has 2 options, giving $2^4 = 16$ distributions. Subtract 2 cases where all birthdays fall in a single month: $16 - 2 = 14$. Favourable cases = $66 \times 14$. Probability = $\frac{66 \times 14}{12^4} = \frac{77}{1728}$.