Chain of honest answers

A bag holds $7$ hats: $3$ red, $2$ white and $2$ blue. $5$ hats are dealt, one to each of $5$ prisoners standing in a line; any colour sequence that can be dealt from the bag is possible. Prisoner $1$ is at the back and sees the $4$ hats in front of him; prisoner $5$ is at the front and sees none. Everyone knows the bag's contents and reasons perfectly. In order from prisoner $1$ to prisoner $5$, each says aloud "I know my colour" or "I do not know", meaning that he can or cannot deduce his own hat colour with certainty from what he sees, the bag's contents and all earlier answers. The colours themselves are never said. For how many possible colour sequences are the $5$ answers, in order: do not know, know, do not know, know, do not know?

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