# Seeing The Red Pin

**Discrete Mathematics**Level 3

A pinsetter is used to replace the bowling pins. There are often more than 10 pins in the machine at any one time to allow for quicker pin setup. Suppose that there are 15 pins in a pinsetter, 14 white pins and 1 red pin. The pinsetter randomly chooses and sets 10 of them on the lane in the typical triangular arrangement. If the probability that the bowler can see the red pin is \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, then what is the value of \(a+b\)?

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