Question

The probability that birthday of twleve people will fall in 12 calender months

Answer 1

hey mate here is your answer

hope you like this answer

The probability of the second person having birthday on a different calendar month of the first person is 11121112, the probability of the third person having a different calendar month birthday than the first two people is 10121012, so on. Therefore the probability of 12 people having their birthdays on different calendar months is 1112×1012×912×⋯×312×212×112=11!12111112×1012×912×⋯×312×212×112=11!1211.

The probability that the third person having birthday on a month either of the first person's or the second person's is 212212, so is the fourth, fifth and sixth since only birthdays on two months are allowed. Therefore the probability that the birthdays of 66 people fall exactly in two months is (16)4(16)4.