Family Seating

[RAHULZ400]

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?

A) 28
B) 32
C) 48
D) 60
E) 120

I have attempted this question in the following manner:

Case1: 2 ways for parents to sit on front seat
2 ways for a daughter to sit on next seat
3 ways for (daughter) for any back seat
2 ways for son for left seats
1 way for parent (left over)

total ways = 2*2*3*2 = 24

Case 2: 2 ways for parent for 1st seat
2 ways for other parent or son to grab the next front seat
2 ways for daughter to sit on 1st back seat
1 way for daughter to sit on 3rd back seat
1 way left for either the left over parent or son

total ways = 2*2*2 = 8 ways

Hence total number of combinations possible = 24+8 = 32

Is this approach fine. Please let me know your feedback.

[RonPurewal]

please search the forum before posting. thank you.

do not post new threads about problems that are already discussed on the forum. after reading through the entire existing thread, please post any remaining questions you might have ON THE SAME THREAD.
thanks.

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