1. Unfortunately, state schools don’t have much in the ________ of sports facilities compared to private schools.
    1. way B. case C. means D. part
I opt “C. means”. However, the answer is “B. case” I don’t know why.
It's a fixed expression, firefly.

They don't have much in the way of facilities. (option A.)

I guess it doesn't make much sense if you haven't grown up hearing it!
Hi,
  1. Unfortunately, state schools don’t have much in the ________ of sports facilities compared to private schools.
    1. way B. case C. means D. part
I opt “C. means”. However, the answer is “B. case” I don’t know why.

The correct answer is 'way'.

. . . not have much in the way of . . . is an idiomatic expression.

eg Tom doesn't have much in the way of money. He has very little money, or even no money.

eg Mary doesn't have much in the way of education. She has very little or no education.

Clive
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Hi, Clive!

Thanks very much for your clear explanation. You are a devoted teacher!
Many thanks to Avangi! You are right! I am not a native speaker, so I haven't grown up hearing this kind of saying.