The pigeon hole principle applies to this situation. If you have 2705 holes and 2706 pigeons at least one hole must have two pigeons in it.
Imelda R. Marcos, a Filipino politician and widow of former Philippine dictator Ferdinand Marcos, is known for her shoe collection; one article talks about the 2705 pairs of shoes in her closet. If Mrs. Marcos' shoe closet is pitch dark and she picks a shoe 2706 times, what is the probability that she has a matching pair to wear?
1. P (matching pair) = 2/2705
2. The event of having a matching pair in this case is the certain event; the probability is one.
3. 2705C2
4. Not enough information
5. 7.39E-4