Probability

Concept:Probability that all 4 birthdays are different is the product of the probabilities that each successive child's birthday is distinct from the previous ones.Explanation:The first child can have any birthday: probability $1$.The second child must have a different birthday: probability $\frac{364}{365}$.The third child must avoid the two already taken: probability $\frac{363}{365}$.The fourth child must avoid the three taken: probability $\frac{362}{365}$.Multiply these: $\frac{364 \times 363 \times 362}{365^3}$.Answer:Option A: $\frac{364 \times 363 \times 362}{(365)^{3}}$