Question 1197462
.
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?
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<pre>
Below in the Table, all possible different numbers of participanting members
are presented, satisfying the imposed conditions.

         T        A        B        L        E

    Professors     Managers    ICT experts   Total

       2              5             3         10
       3              4             3         10
       4              3             3         10


Now write the relevant formulas:

The number of different committees N(2P of 10, 5M from 6, 3E from 8) = {{{C[10]^2*C[6]^5*C[8]^3}}} =  45 *  6 * 56 =  15120,

The number of different committees N(3P of 10, 4M from 6, 3E from 8) = {{{C[10]^3*C[6]^4*C[8]^3}}} = 120 * 15 * 56 = 100800,

The number of different committees N(4P of 10, 3M from 6, 3E from 8) = {{{C[10]^4*C[6]^3*C[8]^3}}} = 210 * 20 * 56 = 235200.


The total numbers of all possible committees is 15120 + 100800 + 235200 = 351120.     <U>ANSWER</U>
</pre>

Solved.


The solution is a simple and almost mechanical procedure.


The problem teaches you to organize your data, your thoughts and your calculations systematically.