Jó napot, Zoltán. If you want to describe a series of items in one sentence using the word "there", the noun that follows is always considered as a singular noun. e.g: There IS a kitchen, a bathroom, and a bedroom in my apartment. If you doubt whether using "is" or "are" in a sentence, you can always rewrite it in another way. e.g.: My apartment has a kitchen, a bathroom, and a bedroom. Hope they help, Tere

Both are grammatically correct. You can say, "there are a man and a woman...," but you will almost NEVER hear that. "There is a man and a woman..." can be thought of as "there is a man and there is a woman in the room." Here's a little more info on that: https://www.englishclub.com/esl-forums/viewtopic.php?t=63809

Hi Zoltán, Your question: "There [is/are] a man and a woman in the room." If we were to deconstruct this sentence, it can also mean "There [is/are] a man and there [is/are] a woman in the room." Very often, in English, writers may provide only as much information as is necessary to convey what they want to express, and this involves leaving out words or phrases so that the sentence does not sound overly formal and stilted, especially in speaking. This is known as Ellipsis. Back to your sentence: "There [is/are]________ a man and there [is/are] _________ a woman in the room.", the answers should be "is" for both "a man" (singular noun) and "a woman" (singular noun). Applying the concept of Ellipsis, I eliminate the extra information "there is" before "a woman". Thus, the final answer becomes "There is a man and a woman in the room." Another example: I asked for a menu but I was given the bill instead! (not wrong, but it can be simplified) I asked for a menu but was given the bill instead! (Ellipsis). I am personally not sure if your first sentence is a possible alternative. However, I will choose your second sentence. I hope this helps

The second one

first