The biblical source for the requirement of ten men to complete a minyan (lit., “count” or “number”) is Numbers 14:27. Moses sent spies to scout the land of Canaan. Ten of them returned and issued a report concluding that it was not a conquerable land. G‑d was extremely disappointed with their lack of faith in His abilities. He turns to Moses and Aaron, telling them: "How long will this evil ‘assembly’ provoke [the Jewish nation] to complain against Me?” From here it is deduced that an “assembly” is comprised of ten men.
Now, in Leviticus 22:32 G‑d says, “I shall be sanctified amidst the children of Israel.” Employing a method of biblical exegesis known as gezerah shavah, wherein two verses with identical terminology are compared to each other, this verse is matched up to another verse (Numbers 16:21): “Separate yourselves from amidst this assembly.” The gezerah shavah teaches us that an “assembly” must be present when G‑d is being sanctified. Examples of such sanctification are the recitation of kaddish, kedushah and barchu, or the public reading of the Torah.
Upon pondering this concept for a moment, one comes to realize a great truth: the power of each individual Jew. There can be a group of nine of the greatest Jews, men who complete all of the commandments and understand the depths of the Torah’s secrets, yet they do not have the ability to complete a minyan on their own. However, add to the group the simplest Jew, someone who perhaps cannot properly read his prayer nor does he relay understand what he is saying, yet when he walks into the room he has now transformed to entire group and made them complete—a minyan. It is because of him that they are now able to recite those parts of the prayer that can be read only with a minyan. Never underestimate the potential of the individual Jew.
I would also suggest that you read a wonderful article entitled Women in the Synagogue.
All the best,
Rabbi Shmuel Kogan,