SOLUTION: A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members  be selected if the team has: 1.. no girl . 2..at least one boy and one girl . 3..at least 3 gir

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Question 849911: A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members  be selected if the team has:
1.. no girl .
2..at least one boy and one girl .
3..at least 3 girls.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The only types of groups of 5 are these:

1.  4 girls, 1 boy     C(4,4)C(7,1) =  (1)(7) =   7 ways 
2.  3 girls, 2 boys    C(4,3)C(7,2) = (4)(21) =  84 ways
3.  2 girls, 3 boys    C(4,2)C(7,3) = (6)(35) = 210 ways
4.  1 girl,  4 boys    C(4,1)C(7,4) = (4)(35) = 140 ways
5.  0 girls, 5 boys    C(4,0)C(7,5) = (1)(21) =  21 ways
--------------------------------------------------------
                                        Total = 462 ways

1. no girl  ==> case 5  DISABLED_event_only= => 21 ways 
2. at least one boy and one girl ==> all cases except case 5 ==> 462-21 = 441 ways
3. at least 3 girls ==> cases 1 and 2  DISABLED_event_only= => 7+84 = 91 ways


Edwin
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