Your wife told you that she saw a friend of hers from college at the grocery store today. You're surprised because your wife went to college in another state far away. You want to show how surprised you are, so you say:
"No way!" is a casual phrase that means "I can't believe it!" Use it when you're surprised and excited about something:
A: Have you been playing the new Call of Duty game?
B: I already beat it.
A: No way!
You can imagine that "No way!" is a shortened version of "There's no way that could be true." Whether or not that's really where "No way!" came from, I don't know.
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