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

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) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
From a group of eight boys and five girls, a boy and a girl will be selected to attend a... (answered by ewatrrr)

from a group of 8 boys and 6 girls, only one of each gender can be chosen to attend the... (answered by Edwin McCravy)

please help me with the Algebra 2 question! From a group of eight boys and three... (answered by sudhanshu_kmr)

Q15 In how many ways can we distribute seven apple and six oranges among 4 children so... (answered by lynnlo)

How many different teams of 5 children can be chosen from a group of 7 boys and 20... (answered by edjones)

There is a group of 19 girls and 13 boys. How many different teams of 4 children can be... (answered by ikleyn)

in how many ways can a group of 5 boys be chosen from a class of twenty boys if the class (answered by Hawksfan)

a. A college debate club comprises of 7 boys and 7 girls. For a debate competition a team (answered by stanbon)

A class consists of 12 boys and 15 girls. How many different committees of four can be... (answered by ikleyn)