To date, about two dozen low-mass embedded protostars exhibit rich spectra with lines of complex organic molecule (COM). These protostars seem to possess different enrichment in COMs. However, the statistics of COM abundance in low-mass protostars are limited by the scarcity of observations. This study introduces the Perseus ALMA Chemistry Survey (PEACHES), which aims at unbiasedly characterizing the chemistry of COMs toward the embedded (Class 0/I) protostars in the Perseus molecular cloud. Of 50 embedded protostars surveyed, 58% of them have emission from COMs. A 56%, 32%, and 40% of the protostars have CH$_3$OH, CH$_3$OCHO, and N-bearing COMs, respectively. The detectability of COMs depends neither on the averaged continuum brightness temperature, a proxy of the H$_2$ column density, nor on the bolometric luminosity and the bolometric temperature. For the protostars with detected COMs, CH$_3$OH has a tight correlation with CH$_3$CN, spanning more than two orders of magnitude in column densities normalized by the continuum brightness temperature, suggesting a chemical relation between CH$_3$OH and CH$_3$CN and a large chemical diversity in the PEACHES samples at the same time. A similar trend with more scatter is also found between all identified COMs, hinting at a common chemistry for the sources with COMs. The correlation between COMs is insensitive to the protostellar properties, such as the bolometric luminosity and the bolometric temperature. The abundance of larger COMs (CH$_3$OCHO and CH$_3$OCH$_3$) relative to that of smaller COMs (CH$_3$OH and CH$_3$CN) increases with the inferred gas column density, hinting at an efficient production of complex species in denser envelopes.
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