Question

How many different professionals committees of 10 people can be formed, each containing at least 2 Professors, at least 3 Managers and 3 ICT Experts from list of 10 Professors, 6 Managers and 8 ICT Experts?

Answer 1

Answer:

616770

Step-by-step explanation:

different possibilities

4 professors , 3 Managers , 3 ICT experts

3 professors , 4 Managers , 3 ICT experts

3 professors , 3 Managers , 4 ICT experts

2 professors , 3 Managers , 5 ICT experts

2 professors , 4 Managers , 4 ICT experts

2 professors , 5 Managers , 3 ICT experts

10c4* 6c3 * 8c3 = 210*20×56=235200

10c3* 6c4 * 8c3 = 120*15*56=100800

10c3* 6c3 * 8c4 =120×20×70=168000

10c2* 6c3 * 8c5 = 45×20× 56 =50400

10c2* 6c4* 8c4 = 45×15×70 = 47250

10c2* 6c5 * 8c3 = 45×6×56 =15120

total = 616770

616770 different professionals committees of 10 people can be formed, each containing at least 2 Professors, at least 3 Managers and 3 ICT Experts from list of 10 Professors, 6 Managers and 8 ICT Experts