Difference between in danger and at risk

[ELAR]

Test No. incompl/advan-79 "GMAT Verbal Quiz (2)", question 8

The local residents in this seaside village are very worried about the constant erosion of the cliff face, which is in ......... of falling into the sea.

(a) risk
(b) chance
(c) danger
(d) likelihood

Test No. incompl/advan-79 "GMAT Verbal Quiz (2)", answer 8

The local residents in this seaside village are very worried about the constant erosion of the cliff face, which is in danger of falling into the sea.

Correct answer: (c) danger

Your answer was: incorrect
The local residents in this seaside village are very worried about the constant erosion of the cliff face, which is in risk of falling into the sea.
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Why no RISK?
ELAR

[Alan]

There are two expressions which are similar in meaning:

IN DANGER and AT RISK and you have to use the first one here because the preposition used in the sentence is in.
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English as a Second Language
You can read my ESL story The way you write it

[nessie]

But what about the phrase "in likelihood of"? I think it is acceptable here...