What is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays?
Given 20 people, what is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays?
hints:
1. to count the number of elements of the state space, look at the following proposition:
There are ( n + r -1 choose r-1 ) distinct nonnegative integer valued vectors
(x_1, x_2, ... , x_3) satisfying
x_1 + x_2 + ... x_r = n
hint 2:
assume that each month has the same number of days, so that the probability that a birthday falls in a particular month is 1/12.