Question 1203152
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A committee of 5 people is to be chosen from 6 midfielders, 3 attackers and 7 referees. 
If each discipline must be represented, determine the number of ways of selecting 
the committee to include: 
(a) exactly one midfielder and one attacker. 
(b) exactly two midfielders; 
(c) at least two midfielders.
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        I will answer  (a)  and  (b),  leaving  (c)  for your own solution/exercise.



<pre>
(a)  In this case, the committee is 1 midfielder, 1 attacker and 5-1-1 = 3 referees.

     THEREFORE, the number of possible committees is  {{{C[6]^1*C[3]^1*C[7]^3}}} = 6*3*35 = 630.   <U>ANSWER</U>



(b)  In this case, the committee is 2 midfielders and 3 persons from ((6+3+7)-2) = 14 other people.

     THEREFORE, the number of possible committees is  {{{C[6]^2*C[14]^3}}} = 15*364 = 5460.   <U>ANSWER</U>
</pre>

Solved.