What's the difference between ぬきで & ぬきの and 入りの & 入りで?

Question

I can't find the difference and in the book that I use there is no explanation.

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Context: It is about ordering food. I have two sentences:

ミルクと砂糖入りの紅茶はいくらですか。
ホットコーヒーをミルクと砂糖入りでください。

Answer 1

Generally speaking, ～で is always adverbial (i.e., modifies a verb), whereas ～の always connects to the following noun. In English this distinction is not always clear because "with ～", "to ～", "in ～" and so on can modify both a noun and a verb.

• ワサビ抜きで寿司を食べた。　I ate sushi without wasabi; I ate, without wasabi, sushi.
• ワサビ抜きで寿司　(sounds like an incomplete sentence fragment because there is no verb for 抜きで to modify)
• ワサビ抜きの寿司を食べた。　I ate sushi without wasabi; I ate wasabi-free sushi.
• ワサビ抜きの寿司　wasabi-free sushi (noun phrase)

When you order something, you can say, for example:

ミルク入りでください。
ミルク入りでお願いします。
With milk, please.

...because ください/お願いします is a verb. You can omit this verb and say this simply:

ミルク入りで。
With milk (, please).

Answer 2

I think you should provide the sentence in the book to get a nice answer.

Probably your book contains the sentence like “彼抜きの会議はつまらない。” or “彼抜きで会議はつまらない” The former normally implies “the meeting without him is boring.”. The latter normally implies “Having a meeting without him is boring.”

Hopefully you could provide some sentences for the distinction 入りの/入りで.