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According to Longman Contemporary Dictionary, out of is used to show how large a part of a group you are talking about, e.g.

Nine out of ten students pass the test first time.

However, I read the following sentence in an English book:

One in five fathers will be househusbands, while the mothers go out to work.

Can the word in be replaced with out of here? And would there be a difference in meaning?

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    in only works with "one". "one in five fathers" but "two/three/four/five out of five fathers". "one in ten students" but "two/three (etc.) out of ten students". out of can also be used with one, though. – user3169 Oct 12 '18 at 5:15
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There is a more exact use of "out of", when the total figure is known, e.g. out of 392 students, 46 were left-handed, however "in" and "out of" are often used interchangeably to talk about a fraction or percentage of a population or total.

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