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Picard is pursued by the Borg while they take over the Enterprise-E. He starts a chapter of some crime-drama holo-novel on the holodeck. The crime boss and his henchmen carry tommy guns, which Picard steals to shoot at the Borg drones. He also turns off the safety protocols on the holodeck so that the bullets are real.

We see that bullets can kill Borg drones.

We know from ST:TNG episodes that physical objects can be removed from the holodeck. (Water in the pilot episode, Encounter at Far Point, and a piece of paper in the episode, Elementary, Dear Data.)

This means Picard should be able to take the tommy guns out of the holodeck to kill the Borg.

Not just that, but he should be able to tell the holodeck to create "guns, lots of guns".

Could Picard have brought the tommy guns out of the holodeck?

Edit to add from comment: Even if Picard can't bring a working tommy gun out of the holodeck, he could still ask the replicators to make tommy guns. That's a good point by Rebel-Scum and still fits within the overall question. Why not use projectile weapons against the Borg?

Could the Borg have adapted quickly to projectile weapons to make that tactic useless?

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    Holodeck guns only work in the holodeck. Perhaps the question is why didn't they just replicate them? – Rebel-Scum Mar 24 '19 at 20:16
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    Why wouldn't they adapt the same way they had to every other attack? – Radhil Mar 24 '19 at 20:32
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    @Rebel-Scum Good point about replicating machine guns. Why not just walk up to a replicator and ask for a tommy gun? I could modify the question to include your point. – RichS Mar 24 '19 at 20:42