Question 1203152: 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.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
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.
(a) In this case, the committee is 1 midfielder, 1 attacker and 5-1-1 = 3 referees.
THEREFORE, the number of possible committees is  = 6*3*35 = 630. ANSWER
(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  = 15*364 = 5460. ANSWER
Solved.
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