Question: Assume that birthdays are equally likely to occur in any one of the 12 months of the year.
a. Given a group of four people, A, B,C, and D, what is the total number of ways in which birth months could be associated with A, B,C, and D? (For instance, A and B might have been born in May, C in September, and D in February. As another example, A might have been born in January, B in June, C in March, and D in October.)
b. How many ways could birth months be associated with A, B,C, and D so that no two people would share the same birth month?
c. How many ways could birth months be associated with A, B,C, and D so that at least two people would share the same birth month?
d. What is the probability that at least two people out of A, B,C, and D share the same birth month?
e. How large must n be so that in any group of n people, the probability that two or more share the same birth month is at least 50%?