Midair Equipment Seating

Great Northern Airlines flies small planes in northern Canada and Alaska. Their largest plane can seat 16 passengers seated in 8 rows of 2. On a certain flight flown on this plane, they have 12 passengers and one large piece of equipment to transport. The equipment is so large that it requires two seats in the same row. The computer randomly assigns seats to the 12 passengers (no 2 passengers will have the same seat). The probability that there are two seats in the same row available for the equipment can be expressed as \( \frac {a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

You may choose to read the blog post on Principle of Inclusion and Exclusion.

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