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Sir,

A good number of festivals,however, are celebrated all over the world.

1. "a good number" means "many'?

2. "are" is for "a good number"?

3. "all over" is adverb or adverbial?

Thanks.
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1. "a number of festivals" is "many festivals". "a good number of festivals" is "very many festivals" (grammatically incorrect).

2. "a number of Xs" is singular in the form, but actually it works as a plural. So they use "are".

3. YES. "all over the world" is an adverbial phrase.

paco
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I would tend to use "a good many" instead of "a good number".

Actually, "a good number" and "a good many" don't exactly mean "very many". The meaning is closer to "a considerable number": a quantity that may not be huge, but is not insignificant.

The following are roughly equivalent in meaning:

We celebrate a considerable number of festivals.
We celebrate quite a few festivals.
We celebrate a good many festivals.
We celebrate a good number of festivals.
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Comments  
I would tend to use "a good many" instead of "a good number".

Actually, "a good number" and "a good many" don't exactly mean "very many". Their meaning is closer to "a considerable number": a quantity that may not be huge, but is not insignificant.

The following are roughly equivalent in meaning:

We celebrate a considerable number of festivals.
We celebrate quite a few festivals.
We celebrate a good many festivals.
We celebrate a good number of festivals.
Students: We have free audio pronunciation exercises.
Hello Dave

Thank you for the comment. I long misunderstood the sense of "a good number of". My bilingual dictionary (Taishukan's Genius English-Japanese dictionary) explains "a good number of" is equal to "a great number of". After reading your comment, I checked the usage of this phrase by using google and OED, and found that the "good" in this phrase should be "considerable" or "rather great" as you told. But now a new question has arisen : which one between "a number of" or "a good number of" does mean a greater number?

paco