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Stockmoose16
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I've posted this difficult probability question from the MGMAT CAT before, but I still don't get it. Can an expert please analyze my logic and explain why it's wrong?
A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
The first constraint is that one of the parents must drive. So I figured out the possible # of seating arrangements, given this constraint:
2 parents can drive the car
4 people (B, G1,G2, non-driving parent) can sit in the passenger seat
3 people (remaining after filling passenger seat) can sit in left back seat
2 people (remaining after filling left back seat )can sit in middle back seat (persons r
1 person (remaining after filling all other seats) can sit in right back seat
Constraint #1: Total # of seating options: 2*4*3*2*1 = 48
Now, you have to subtract out the second constraint -- the girls can't sit next to each other: (calculated by finding the # of ways the girls DO sit next to each other)
2 parents can drive the car
2 people (Boy, non-driving parent) can sit in the passenger seat [girls must sit in back seat to be next to each other)
3 people (G1, G2, Parent/Boy [whomever wasn't selected for passenger seat]) can sit in left back seat
2 persons (assuming boy was selected for left back seat, either of the girls can sit in the middle)can sit in middle back seat
1 person (remaining girl, after filling all other seats) can sit in right back seat
=2*2*3*2*1= 24
My answer is 48-24= 24
The OA is 32.
What am I doing wrong? Where is my logic flawed? Please specifically point out my error (rather than just showing how to do the problem correctly).
A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
The first constraint is that one of the parents must drive. So I figured out the possible # of seating arrangements, given this constraint:
2 parents can drive the car
4 people (B, G1,G2, non-driving parent) can sit in the passenger seat
3 people (remaining after filling passenger seat) can sit in left back seat
2 people (remaining after filling left back seat )can sit in middle back seat (persons r
1 person (remaining after filling all other seats) can sit in right back seat
Constraint #1: Total # of seating options: 2*4*3*2*1 = 48
Now, you have to subtract out the second constraint -- the girls can't sit next to each other: (calculated by finding the # of ways the girls DO sit next to each other)
2 parents can drive the car
2 people (Boy, non-driving parent) can sit in the passenger seat [girls must sit in back seat to be next to each other)
3 people (G1, G2, Parent/Boy [whomever wasn't selected for passenger seat]) can sit in left back seat
2 persons (assuming boy was selected for left back seat, either of the girls can sit in the middle)can sit in middle back seat
1 person (remaining girl, after filling all other seats) can sit in right back seat
=2*2*3*2*1= 24
My answer is 48-24= 24
The OA is 32.
What am I doing wrong? Where is my logic flawed? Please specifically point out my error (rather than just showing how to do the problem correctly).
