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Question:

What type of vulnerability must be present to make this remote attack possible in the following?
Several unexpected files are discovered in the root directory of a network administrator's Linux FTP server. One file is a tarball, two are shell programs, and the third is a binary file called 'nc.' The anonymous user account logged in to the FTP server, uploaded the files, extracted the contents of the tarball, and ran the script using a feature offered by the FTP server's software, according to the access logs. The ps command indicates that the nc file is running as a process, and the netstat command indicates that the nc process is listening on a network port.

A File system permissions
Explaination