Is it grammatically correct to use "was no"?

[LizzyBennet]

I did a gapped text task where I came across the following sentences: "The big music story of 2005 turned out to be the success of the Arctic Monkeys, a British group whose debut single went straight to the top of the charts. But theirs was...ordinary success story in the music business."
I filled the gap "was...ordinary" with "not" and was surprised because the correct answer was "no" (But theirs was no ordinary success story in the music business). Why so? Is it the definite rule to use "no"?
Thanks in advance!

[euncu]

If there was "an" before "ordinary", "not" would be correct.

[kfredson]

I did a gapped text task where I came across the following sentences: "The big music story of 2005 turned out to be the success of the Arctic Monkeys, a British group whose debut single went straight to the top of the charts. But theirs was...ordinary success story in the music business."
I filled the gap "was...ordinary" with "not" and was surprised because the correct answer was "no" (But theirs was no ordinary success story in the music business). Why so? Is it the definite rule to use "no"?
Thanks in advance!

It may be clearer if you think of it as the following:
Their story was no success story, which is the opposite of
Their story was a success story.

As mentioned by euncu, no could be replaced by "not a".

As I understand it, in such situations we use "no" when we want to emphasize the negative.

[RonBee]

no ordinary success story = not an ordinary success story

[nuharani]

no ordinary success story = not an ordinary success story

So, can I say both: 1.This is no smoking area or 2. This is not a smoking area
Thanks.

[mxreader]

So, can I say both: 1.This is a no smoking area or 2. This is not a smoking area
Thanks.

[Raymott]

So, can I say both: 1.This is no smoking area or 2. This is not a smoking area
Thanks.

No you can't. You need 'a' in both sentences.
In the vast majority of cases, 'not a' cannot be replaced by 'no' and vice versa. It only applies to this construction.

It's usually used in sentences such as this:
1. I like words, but I'm no linguist.
2. I play tennis, but I'm no Roger Federer.
3. Chopin was no ordinary pianist.

"I'm not a linguist" is a mere statement of fact. "I'm no linguist" means something like "Please don't assume I know much about linguistics".
It can mean "not any kind of" or "nowhere near as good as" (1. and 2.)
In 3. it has an intensifying effect.