SOLUTION: assume there are 365 days in a year, from a group of 4 random people a) what is the total number of combination for their birthday b)what is the total number of combination for t

(a)  In a random sample of 4 people, 

        - any of the 365 days can be a birthday for the 1st person;
        - any of the 365 days can be a birthday for the 2nd person;
        - any of the 365 days can be a birthday for the 3rd person;
        - any of the 365 days can be a birthday for the 4th person.

     So, the total number of all possible different combinations for their birthdays is  .



(b)  If no birthday is shared by any two people, then the number of all possible different 
     combinations for their birthdays is  365*364*363*362.

     (365 possibilities for the 1st person; 364 for the 2nd person and so on . . . )



(c)  Using the formulas from (a) and (b), you can deduce the answer for (c)

         P(c) =  =  = 0.9836 (rounded).


(d)  The probability in (d) is the COMPLEMENT to that in (c)

         P(d) = 1 - P(c) = 1 -  = 1 - 0.9836 = 0.0164  (rounded).