You want to permit a user to change the passwords of certain other users.
To permit smith to change the passwords of jones, chu, and agarwal:
/etc/sudoers: smith ALL = NOPASSWD: \ /usr/bin/passwd jones, \ /usr/bin/passwd chu, \ /usr/bin/passwd agarwal
The NOPASSWD tag is optional, for convenience. [Recipe 5.4]
As another example, permit a professor to change passwords for her students, whose logins are student00, student01, student02,...up to student99.
/etc/sudoers: prof ALL = NOPASSWD: /usr/bin/passwd student[0-9][0-9]
Note that this uses shell-style wildcard expansion; see sudoers(5) for the full syntax.