# 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?

1
by sahu93narendra

2015-10-08T20:20:19+05:30

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The 8 members team can be either of the following:
a. 3 professor, 2 technical managers and 3 database expert
Total ways of choosing this =10C3*8C2*10C3=120*28*120=403200

b. 2 professor, 3 technical managers and 3 database expert
Total ways of choosing this =10C2*8C3*10C3=45*56*120=302400

c. 2 professor, 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.