Soru

In a district administration office, a survey of $120$ officers was conducted regarding their proficiency in using three government portals: e-Office ($E$), CPGRAMS ($C$), and GeM ($G$). The survey revealed that $65$ officers are proficient in e-Office, $55$ in CPGRAMS, and $50$ in GeM. Furthermore, $25$ officers are proficient in both e-Office and CPGRAMS, $20$ in both CPGRAMS and GeM, and $22$ in both e-Office and GeM. If $10$ officers are proficient in all three portals, how many officers are proficient in none of these three portals?