I am assuming that your ORACLE_BASE is /oracle so did you create a 10g subdirectory under that? It's a little strange that even though you have set your ORACLE_HOME environment variable, it still wants to install in your existing ORACLE_HOMEs. Check to ensure that your ORACLE_HOME variable is, in fact, pointing to /oracle/10g by using the echo command:
echo $ORACLE_HOMERemember that setting this is session-specific, so once this variable is set use that session to begin your installation.
One more thing to keep in mind is that If you have attempted to install the Oracle 10g software into this home before and it has failed, there will be residual files left in this ORACLE_HOME, most likely inventory files. You can either delete these files before you start or when the installer detects them, choose to continue the installation process and those files will be overwritten.
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