"A majority of" goes with count nouns. It can quantify "people," but not "money."

Both "a majority of people" and "a majority of the people" are correct, depending on the context.

The guidelines for the use of the definite article with "people" in this phrase are the same as the use of the article for count nouns in general. For instance, in expressions of quantity, when referring to a general group, the definite article is often omitted, as in these examples from Google:

A majority of people with severe and profound hearing loss will ...
A majority of people, 55 percent, said they'd be willing to reduce material possessions and earnings by "some" or "a lot" to gain time with family and to ...
"¢ ... A majority of people with children would use an extra 1000 to pay off bills...while people with no children would sock it in the bank or spend it. ...

When referring to a specific group, the definite article is usually included, as in these examples from Google:

"¢ Are tattoos a show of conformity? In many cases, yes. A majority of the people on the street today have the tattoos that only twenty years ago, scared parents. ...
"¢ ... Behavior may be banned merely because a majority of the people don't like it, not because there is anything intrinsically wrong with it. ...
"¢ ... people are still uncertain, 15 percent. A majority of the people,49 percent, is against EMU. However, the number of people who ...

There are additional considerations for including or excluding the definite article with "people," such as first mention or second mention. To answer your question, though, both "a majority of people" and "a majority of the people" are possible.
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There is a meaning of "people" that does take the article, whether it refers to a general or a specific meaning: the meaning of "people" as a population, as in these examples:

"¢ ... Despite this, a big share of the actions and decisions of the government and its members are opposed by a majority of the people, and the government uses its ...
"¢ The basic principle of the amendment is that our leaders should be supported by a majority of the people. ...
"¢ ... Walter Judd, our US Congressman from 1942-1962 said, "People often say that, in a democracy, decisions are made by a majority of the people. ...
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With noncount nouns, use a different expression, such as "most money" or "most of the money," or "the greatest amount of money."

Rachel

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