There is...

a) There _____ a man, a lady and some children in the park.
The blank should be filled with is or are ???

In some grammar books, I've read the following sentences:

b) There’s a chair and a table in the room.
c) There’s a chair and two tables in the room.
d) There are two tables and a chair in the room.

I don’t have any doubt on (d) but as to (a),(b) and ©…

Please,could you explain the rule from a point of strictly grammatical view?

I don’t have a very good answer, but it seems to me that “there is”, when expressing existence, is practically an idiomatic expression rather than one that needs to follow strict grammatical rules. In colloquial speech, “there’s” has an even stronger tendency than “there is” to be used irrespective of number, and it is not uncommon to hear sentences like “There’s two chairs in the room”, which in informal contexts are acceptable to many native speakers.

Hi Alan, Esl_Expert!
Would you please express your professional opinions on this?