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"Selection" is a word like family, team, band etc where it can refer to the thing itself (singular) or the individual parts (plural). In some cases either can be correct, depending on what you want to emphasise.
You're referring to the individual parts so it's plural. That's also a nicer sounding sentence.
grams
A random selection of households are being asked to participate
or
A random selection of households is being asked to participate