Anywhere from 4-6. But, the most common one has 5
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The plectrum banjo has four strings, lacking the shorter fifth string, and 22 frets; it is usually tuned CGBD. As the name suggests, it is usually played with a guitar-style pick (that is, a single one held between thumb and forefinger), unlike the five-string banjo, which is almost always played with a thumbpick and two fingerpicks, or occasionally with bare fingers. The plectrum banjo evolved out of the five-string banjo, to cater to styles of music involving strummed chords.
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The origins of the five-string banjo are often, but possibly erroneously, linked to Joel Walker Sweeney, an American minstrel performer from Appomattox Court House, Virginia. Sweeney wanted an instrument similar to the banjar played by African Americans in the American South, but at the same time, he wanted to implement some new ideas. He worked with a New York drum maker to replace the banjar's skin-covered gourd with the modern open-backed drum-like pot, and added another string to give the instrument more range or a drone. This new banjo came to be tuned gCGBD; somewhat higher than the eAEG#B tuning of the banjar. However, a painting done long before Sweeney's supposed invention of the fifth string, called The Old Plantation, shows African American slaves playing a banjo that has what appears to be three long strings and a short, thumb-plucked string. In part because of that painting, modern scholarship now believes that it was the bass string that Sweeney added, not the "thumb string".
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The six-string or guitar-banjo was the instrument of the early jazz great Johnny St. Cyr, as well as of jazzmen Danny Barker, Papa Charlie Jackson and Clancy Hayes. Nowadays, it sometimes appears under trade names such as "banjitar".