FINDING BIRTHDAY TWINS

If you randomly select a group of just $21$ people the chance of there being a pair of people with the same birthday is greater than $50\%$. This surprising fact is due to the large number of pairings possible in a group of $21$ people.

1. Determine the number of possible unique pairings in a group of $21$ people.

   Hint (a):

   Unique pairings refer to the number of combinations of $2$.

2. Compute the probability that any given pair of people have the same birthday (ignoring leap day).

   Answer (b):

   $\left(\frac{1}{365}\right)=0.002740$

3. Compute the probability that any given pair of people do not have the same birthday (ignoring leap day).

   Hint (c):

   See part (b).

4. Now compute the probability that exactly one pair out of the $21$ people has the same birthday.

   Hint (d):

   Use the answers from parts (a) – (c) to determine the probability.