Question 256382: What is the formula for solving this? "If you have a class consisting of 10 girls and 20 boys, in how many different ways can you form a committee from the class members such that there will be 2 girls and 2 boys on the committee?"
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula is:
c(10,2) * c(20,2)
that's (10! / (2!8!)) * (20!/(2!18!))
that becomes:
(10*9/2*1) * (20*19/2*1) which equals 45*190 = 8550
to see this in action, assume this was 3 girls and 4 boys and you want a committee of 2 girls and 2 boys.
number of possible combinations for girls is c(3,2) = 3!/2!1! = 3
assume the girls are abc.
then you get possible combinations of:
ab
ac
bc
anything else would be a duplicate. example: ba is the same combination of ab because order is not considered. if order was considered, it would be a permutation.
for the boys, the possible combinations would be c(4,2) = 4!/2!2! = 6
if the boys are defg, thenpossible combinations are:
de
df
dg
ef
eg
fg
now, for each combination of girls, you get 6 combinations of boys, which means a total of:
c(3,2)*c(4,2) = 3 * 6 = 18
these combinations would be:
ab + de
ab + df
ab + dg
ab + ef
ab + eg
ab + fg
ac + de
ac + df
ac + dg
ac + ef
ac + eg
ac + fg
bc + de
bc + df
bc + dg
bc + ef
bc + eg
bc + fg
same principle applies for the bigger figures, so your answer should be as stated above.
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