1. The printer ran out of ink.
2. The printer has run out of ink.
3. We're out of ink.
All are correct. The third sentence has a different meaning.
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1. The printer ran out of ink. This tells us about an event in the past. Maybe it happened 2 minutes ago or maybe 2 years ago. It does not tell us whether the printer now has ink.
2. The printer has run out of ink. This tells us the printer now has no ink.
3. We're out of ink. We have no ink.