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ashdank94
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ashdank94
Interesting :) it wasn’t specified in the question that daughters have to sit in the back so I assumed it was a shotgun situation lol
­Haha. Yeah, the idea is that they can't sit "next to each other" in one front seat.
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Assuming front and back in the same line are not considered together

The daughters can choose the 2 out of 4 seats in 4C2 = 6 ways, of which in 2 cases they are together (both at the back)
So, favourable seat selection is 4. Also, the driver can be selected in 2 ways
Now, for the arrangements - the daughters can arrange in 2! ways and the other 2 people in 2! ways

Total = 4*2*2*2 = 32 (B)


pratikbais
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
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I have a question - why do we treat this question as if we are using permutations with repetitions? In the reverse logic, we use 2! * 2 to seat 2 daughters together and one person with them at the back and in drivers seat we put 2 for M/D, but then in the front seat we are putting 2 but isnt only per person left now for front seat. If one has already sat at the back then why aren't we using 1 in the front seat?
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I have a question - why do we treat this question as if we are using permutations with repetitions? In the reverse logic, we use 2! * 2 to seat 2 daughters together and one person with them at the back and in drivers seat we put 2 for M/D, but then in the front seat we are putting 2 but isnt only per person left now for front seat. If one has already sat at the back then why aren't we using 1 in the front seat?

The 2 for the front seat is correct because at that stage no one else has yet been assigned to the remaining back-seat spot. After fixing the driver and the two daughters together in the back, there are 2 people left, and either of them can take the front seat, with the other automatically taking the last back seat.
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