SOLUTION: a group of five children has to be chosen from a form of eight boys and twelve girls.in how many ways can the selection be made if the group must contain at least two boys and two

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Question 962557: a group of five children has to be chosen from a form of eight boys and twelve girls.in how many ways can the selection be made if the group must contain at least two boys and two girls?
Answer by Edwin McCravy(20054) About Me  (Show Source):
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a group of five children has to be chosen from a form of eight boys and twelve girls.in how many ways can the selection be made if the group must contain at least two boys and two girls? 
That's either 3 girls and 2 boys or 2 girls and 3 boys.

Case 1:  3 girls and 2 boys

Choose the 3 girls 12C3 = 220 ways and the 2 boys 8C2 = 28 ways.
That's 220*28 = 6160 ways.

Case 2:  2 girls and 2 boys

Choose the 2 girls 12C2 = 66 ways and the 3 boys 8C3 = 56 ways.
That's 66*56 = 3696 ways.

Grand total 6160+3696 = 9856 ways.

Edwin