Help With Allocative Efficiency?

There’s a question I need some help with, I really don’t get it.
First there’s a little piece of text:
‘In some areas of the country, some state schools are over-subscribed. This means that there are more children wanting to come to the school than there are places available. In such circumstances schools have to choose their children according to admission rules. Typically these are based on catchment areas. Children who live close to the school get in. This might not be the most efficient way of allocating places. Some economists have advocated giving each child in the country a voucher worth £X which is handed over to their school and then cashed in to pay for the expenses of running the school . Oversubscribed schools could charge fees over and above the value of the voucher. The size of the fee would be fixed to limit the number of entrants to the school to the number of places offered. Just as in, say, the second hand car market, if some cars are more popular than others then car sellers can charge higher prices, so would be the case in the education market. Resources will thus be efficiently allocated.’
(a) Why might it be argued that there is allocative inefficiency in areas where some schools are oversubscribed?
(b) What might be the advantages and disadvantages to introducing a voucher and fee system in education?
I don’t get the piece of text, what is the proposition? Would answer to part (a) have something to do with there being schools in sparsely populated areas? I don’t understand (b) either, that would be privatising education, and therefore those who have fewer financial resources would be put at should not be bought, education is the staple to a progressive healthy society and everyone should have the right to it.
I’m really not getting these questions or what they’re about.
Please help.

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