Game of Chance

John chooses 22 numbers randomly without replacement from a bag containing the first 1010 positive integers, leaving 8 numbers. Then, Mark chooses 22 numbers randomly without replacement from the bag, which leaves 6 numbers. John wins if, among the 44 numbers picked, he picked both the largest and the smallest. If the probability John wins can be expressed as ab\dfrac{a}{b}, find a+ba+b.

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