Question 1194947: Please help me solve this word problem using Combinations:
A quiz team of 5 children is to be selected from a class of 24 children. There are 14 girls and 10 boys in the class.
(a) How many teams made up of 3 girls and 2 boys can be selected?
teams
(b) How many teams can be selected with at least 3 girls?
teams
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are 14 girls and 11 boys.
the number of ways you can get a team of 5 children where 3 are girls and 2 are boys is equal to c(14,3) * c(11,2) = 20,020.
the number of ways you can get a team of 5 children where at least 3 are girls is equal to c(14,3) * c(11,2) + c(14,4) + c(11,1) + c(14,5) * c(11,0) = 20,020 + 11,011 + 2,002 = 33,033.
c(n,x) is equal to n! / (x! * (n-x)!)
for example:
c(14,3) = 14! / (3! * 11!) which is equal to:
(14 * 13 * 12 * 11!) / (3! * 11!) which is equal to:
(14 * 13 * 12) / (3 * 2 * 1) which is equal to:
2184 / 6 which is equal to 364.
and:
c(11,2) = 11! / (2! * 9!) which is equal to:
(11 * 10 * 9!) / (2! * 9!) which is equal to:
(11 * 10) / (2 * 1) which is equal to:
110 / 2 which is equal to 55.
therefore:
c(14,3) * c(11,2) is equal to 364 * 55 = 20,020.
answers to your questions are:
(a) How many teams made up of 3 girls and 2 boys can be selected?
number of teams = 20,020.
(b) How many teams can be selected with at least 3 girls?
number of teams = 33,033.
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