We have two ways of forming the expression “there’s no way that…” or “it’s impossible that…”—わけがない and はずがない.

【Verb】【わけがない or はずがない】
パスタでもできないから、ティラミスが作れるわけがありません。
I can’t even do pasta so there’s no way I can make tiramisu.
彼が知らないわけがない。
There’s no way he doesn’t know.
簡単な問題だから数学が得意な君はできないわけがないよ。
It’s an easy problem so there’s no way that someone good at maths like you can’t solve it.
自分のことで精一杯で、あなたのことに構ってあげられるわけがない。
I’m up to my eyes in my own things so there’s no way I can give you attention.
最近、彼女はへこんでいるみたいだよ。彼氏ができるわけがないとかって言ってるし。
Lately she’s seem to be feeling down-hearted. She’s saying stuff like there’s no way she can get a boyfriend.

The subject particle が is often omitted in casual conversation.

そんなお金あるわけないだろ。
There’s no way I’d have that sort of money.
だって、まだ仕事だもん。今夜は飲み会に行けるわけない!
You know, I’m still at work. There’s no way I can go to the drinks tonight!
こんな立派なテレビが安いわけがない。
Such an awesome television—there’s no way it’s cheap.

We can form exactly the same expression with はず instead of わけ. Used with はず the phrase is a little more formal.

事故が目の前で起ったので、気づかなかったはずがないでしょ。
The accident happened right in front of you so it’s impossible that you didn’t notice.

はず can also be treated as a noun and connected to other nouns with the possessive particle. わけ always follows a verb.

彼は本気のはずがないでしょう。
He can’t be serious.

わけがない can also come off as a little brash, which is why in more formal speech はず would normally be used. For instance, if in a restaurant a waiter mistakenly brought you a beer when you don’t even drink alcohol you might say:

私はお酒が飲めないので、ビールを注文したはずがないんですが。
I cannot drink alcohol so I cannot have ordered beer.

Note the use of んですが at the end to tone down the sentence.

Note the very different meaning of わけがない and わけではない which was introduced here. Take care not to confuse the two.

彼女に勝てるわけがない。
There’s no way I could beat her.
彼女に勝てるわけじゃない。
That doesn’t mean I can beat her.
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