Ten men form a Minyan only if they are all assembled in the same room. If the ten are interspersed among two rooms, then even if there is no door between the two adjoining rooms, and they can all see each other, they do not form a Minyan. (However, if ten men are situated together in one room, then others who are situated in the adjoining room are considered to pray with a Minyan.)
The Tur (Rabbenu Yaakob Ben Asher, 1269-1340) cites his father, the Rosh (Rabbenu Asher Ben Yehiel, Germany-Spain, 1250-1327), as making an interesting exception to this rule. He asserts that if five men are in one room, and five others are in an adjoining room, they combine to form a Minyan if the Hazzan stands in the doorway between the two rooms. As long as all ten men can see the Hazzan – even if they cannot see each other – they are considered a Minyan, as the Hazzan in this case combines them together.
Several Poskim extended this Halacha to apply in a case where nine people are in a room, and the Hazzan stands in the entranceway to the room. Normally, a man who stands in the doorway cannot be counted toward the Minyan together with those inside the room. However, if it is the Hazzan standing in the doorway, then, according to this opinion, he combines with nine men inside to form a Minyan. This view is advanced by Rabbi Akiva Eger (1761-1837), who argued that if a Hazzan standing in a doorway between two rooms can combine the men in the two rooms to form a Minyan, then certainly he himself can combine with the nine men of the room when he stands in the doorway. This is the view also of the Perisha (Rav Yehoshua Falk, d. 1614). By contrast, the Peri Megadim (Rav Yosef Teomim, 1727-1792) argued that the Rosh's ruling cannot be extended to the case of a Hazzan standing in the doorway with nine men in the room.
The Mishna Berura accepts the lenient ruling of Rabbi Akiva Eger and the Perisha. This is the conclusion also of Hacham David Yosef, in Halacha Berura, who noted that different views exist regarding the status of a person standing in a doorway. Although Halacha follows the opinion that he cannot be counted together with the people standing in the room, nevertheless, the opposing view creates a "Sefek Sefeka" – a situation where two Halachic uncertainties are at play. To begin with, there are those who allow counting a person standing in the doorway, and even according to the stringent opinion, some Poskim allow counting him if he is the Hazzan. Hence, we can rely on this leniency, and allow nine men to form a Minyan with a tenth man in the doorway if that tenth man is the Hazzan.
Summary: If ten men are together in two adjoining rooms, with some in one room and some in the other, they do not form a Minyan, unless the Hazzan stands in the doorway connecting the two rooms, and everyone in both rooms can see him. Similarly, if nine men are in a room and a tenth man is in the doorway, the tenth man can be counted if he is the Hazzan.