Select the option that expresses the given sentence in passive voice.…

The correct answer is Option (3) → The bamboo bridge near our village could have been washed away by the swollen river.

Passive of “could have” + past participle (V3):

Change	Active	Passive	Why
Object becomes subject	the bamboo bridge near our village	The bamboo bridge near our village	The bridge receives the action, so it becomes the subject.
Modal and tense kept	could have washed away	could have been washed away	“Could have washed away” talks of something possible in the past. The passive keeps “could have” and adds “been”: could have been + past participle (V3). “Away” stays with “washed”.
Agent (by ...)	The swollen river	by the swollen river	The river is named, so the doer comes after “by”.
Full sentence	The swollen river could have washed away the bamboo bridge near our village.	The bamboo bridge near our village could have been washed away by the swollen river.

“Might have” and “would have” work the same way: might have + V3 → might have been + V3. Example: The wind might have blown down the signboard. → The signboard might have been blown down by the wind.

Why the Other Options are Incorrect?

Option 1: The bamboo bridge near our village could be washed away by the swollen river. — Incorrect. “Could be washed away” talks of now or later. “Have” is dropped, so the past idea is lost.

Option 2: The bamboo bridge near our village could have washed away by the swollen river. — Incorrect. The word “been” is missing. Without it, the verb is not passive.

Option 4: The swollen river could have been washed away by the bamboo bridge near our village. — Incorrect. This turns the meaning around. Now the bridge washes away the river.