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
OA is 32.
I got 48 ways to seat people (2*4*3*2*1) ways. However I could count only 12 seating arrangements to deduct from 48 for those events in which daughters occupied adjacent seats.
Could someone clarify?
Sedan Holiday
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 shovan85
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Total Ways = Driver seat (2 ways) * 4 * 3 * 2 = 48 ways
Say the two sisters sit together S1 and S2
S1,S2 sequence possible ways = Driver seat (2 ways) * Next Front Seat (2 ways other parent and son) * Back remaining 1seat (2 ways son and other parent) * rest 2 back seats (1 way) = 8 ways
Now, change the arrangement of Sisters to S2,S1 = 8 ways
Total number of ways when both sisters sit together = 2*8 = 16 ways
Number ways they do not sit together = 48  16 = 32 ways
Say the two sisters sit together S1 and S2
S1,S2 sequence possible ways = Driver seat (2 ways) * Next Front Seat (2 ways other parent and son) * Back remaining 1seat (2 ways son and other parent) * rest 2 back seats (1 way) = 8 ways
Now, change the arrangement of Sisters to S2,S1 = 8 ways
Total number of ways when both sisters sit together = 2*8 = 16 ways
Number ways they do not sit together = 48  16 = 32 ways
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I see the mistake in my working now.
I had not calculated 4 possible ways in which sisters would sit next to each other in the front seats.
So 12+ 4 = 16
!!
Thanks
I had not calculated 4 possible ways in which sisters would sit next to each other in the front seats.
So 12+ 4 = 16
!!
Thanks