Candice returns home

Discrete Mathematics Level 5

After rattling her brain with combinatorics, Candice finally decides how she wants to buy her candy. She bought what she wanted and was on her way home when she stumbles across a \($100\) note on the pavement.

Candice, being the innocent little child she is, decides to take the note. She notices that the note is numbered \( AWK45 \).

If the probability that she has touched this note before is \( x\), evaluate \( \lfloor 10^5 x \rfloor \).

Details and assumptions

  • Each note is labelled in the form \(LLLNN\) where L represents a letter and N represents non-negative integer less than 10.
  • Assume this currency is limited to only \($100\) notes and that each possible note is currently in circulation. There is equal probability of this being any one of the notes.
  • Candice is 10 years old. Assume that every note her mother earns from the moment she is born touches her hand. These do not have to be unique.
  • Her mother makes exactly \($100000\) a month.
  • You are allowed to use a calculator. Do not make any extra assumptions.
Thanks to Calvin Lin for helping with the problem.
Image Credit : barryfromtexas on Photobucket.
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