HELP!! Probability

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

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.

but there are 2705 PAIRS .. so 5410 actual shoes...

Quote:

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Originally Posted by jthomp18

but there are 2705 PAIRS .. so 5410 actual shoes...

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So okay. Lets suppose she is really unlucky and draws 2705 shoes all different. She has one of every pair. What must happen on the next selection.

2705C2 = 3657160? right?