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family

by ricky » Tue Aug 05, 2008 1:34 pm
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?
28
32
48
60
120
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by parallel_chase » Tue Aug 05, 2008 2:28 pm
This problem can be done in many ways. I will show 2 ways.

First method.

Case I (both girls sit at the back seat)
No. of ways father or mother can be arranged in driver's seat = 2 ways
No. of ways either of parent and son can be arranged in front seat= 2 ways
No. of ways one girl can be arranged in the first back seat= 2 ways
No. of ways boy can can be arranged in second back seat= 1 way
No. of ways last girl can be arranged in third back seat = 1 way

2*2*2*1*1 = 8

Case II (1 girl sit in the front)
No. of ways father or mother can be arranged in driver's seat = 2 ways
No. of ways either of the girls can be arranged in front seat= 2 ways
1 son, 1 parent & 1 girl can be arranged in back seat = 3! or 6 ways

2*2*6 = 24

24+8=32 ways

Second method

Total number of combinations in which entire family can be arranged
2 for driver's seat
4 for 2 girls, 1 son & either of the parent
remaining can be arranged in 3! or 6 ways at the back.

2*4*3*2*1 = 48 ways

Total number of combinations in which two girls are sitting together =
2 for the driver's seat
2 for either of the parent and son
2! or 2 for girls sitting together at the back
2 for 2 seats left for either the parent or son

2*2*2*2 = 16


48-16 =32

Let me know if you still have any doubts.
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by ricky » Tue Aug 05, 2008 3:26 pm
Thanx Buddy..its clear now
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