How many different 8 professionals committees can be formed each
containing at least 2 Professors, at least 2 Technical Managers and 3
Database Experts from list of 10 Professors, 8 Technical Managers
and 10 Database Experts?
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The 8 members team can be either of the following
a) 3 professors, 2 technical managers, and 3 database experts.
Total ways of choosing this
= 10C3 × 8C2 × 10C3
= 120 × 28 ×120
=403200//
b) 2 Professors, 3 technical managers, and 3 database experts.
Total ways of choosing this
= 10C2 × 8C3 × 10C3
=45 × 56 × 120
=302400//
c) 2 Professors, 2 technical managers and 4 database expert.
Total ways of choosing this
= 10C2 × 8C2 × 10C4
= 45 × 28 × 210
= 264600//
Total ways =403200 + 302400 + 264600
=970200//
Total ways is 970200//
a) 3 professors, 2 technical managers, and 3 database experts.
Total ways of choosing this
= 10C3 × 8C2 × 10C3
= 120 × 28 ×120
=403200//
b) 2 Professors, 3 technical managers, and 3 database experts.
Total ways of choosing this
= 10C2 × 8C3 × 10C3
=45 × 56 × 120
=302400//
c) 2 Professors, 2 technical managers and 4 database expert.
Total ways of choosing this
= 10C2 × 8C2 × 10C4
= 45 × 28 × 210
= 264600//
Total ways =403200 + 302400 + 264600
=970200//
Total ways is 970200//
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