Bowl of Cherries VI

EasyProbability

Each of 16 distinct cherries has an equal chance of being placed into one of 4 distinct bowls. Let $a$ equal the probability that one bowl has 3 cherries, another has 5 cherries, and the remaining bowls contain 4 cherries each. Let $b$ denote the probability that all bowls contain 4 cherries each. What is $\frac{a}{b}$ ?

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