How I solved this (in case the logic helps someone!)(1) What is required? We need either 2 or 3 girls in one of the 3 cars.
What are the possible scenarios? a) 1 car with 3 girls (GGG), then, the other two cars have only boys (BB, BBB).
b) 1 car with exactly 2 girls (GG), then, the other 2 cars are (GBB, BBB) (one of the remaining girls in one of the two remaining cars).
c) 1 car with 2 girls and a boy (GGB), the other 2 cars can have either ->
------> GB and BBB or
------> BB and GBB
(2) First, from the 3 cars, let us select the car that will have only 2 children in it.
3C1 = 3 ways to fix this car.(3) Now, from the remaining 2 cars (which will have 3 children), we need to fix the car where we will ->
a) either have 3 girls
(GGG) or
b) have the remaining girl after assigning 2 girls to the car having only 2 girls (GG
GBB BBB) or
c) have 2 girls and a boy
(GGB) For all the above purposes, we will need to choose one car from the 2 remaining cars.
2C1 = 2 ways to fix this other car. Now that we have estimated the number of ways the cars can be selected for our purposes (3 ways to select the 2-seater, and 2 ways to select the main 3-seater = 3 x 2 = 6 ways total), we can focus on estimating the ways in which girls and boys can be selected to fill the cars, based on the scenarios above.(4) GGG;BB;BBB -> (3C3) x (5C2) x (3C3) = 1 x 10 x 1 =
10 ways.
(5) GG;GBB;BBB -> (3C2) x (1C1 x 5C2) x (3C3) = 3 x 1 x 10 x 1 =
30 ways.
(6) GGB;GB;BBB -> (3C2 x 5C1) x (1C1 x 4C1) x (3C3) = 15 x 4 x 1 =
60 ways.
(7) GGB;BB;GBB -> (3C2 x 5C1) x (4C2) x (1C1 x 2C2) = 15 x 6 x 1 =
90 ways.
(8) Total number of ways of accomodating either 2 or 3 girls in one of the cars = Number of ways of selecting the cars x Number of ways of selecting the children to place in the cars
Total number of ways of accomodating either 2 or 3 girls in one of the cars = (2) x (3) x
[ (4) + (5) + (6) + (7) ]= 3 x 2 x [ 10 + 30 + 60 + 90 ] = 6 x [ 190 ] =
1140. Choice B. ___
Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website:
gmatanchor.com