If the coefficient of \( a^{7} b^{8} \) in the expansion of \( (a+2...

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If the coefficient of \( a^{7} b^{8} \) in the expansion of \( (a+2 b+4 a b)^{10} \) is \( K 2^{16} \), then \( K \) is equal to _________.
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