gmatkudi wrote:

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

Total # ways possible (with only one constraint of one parent sitting in front)

= 4! *2 = 48

# ways, when both the daughters are sitting together: (P1-Parent1, P2- Parent2, S-Son, D- Daughter)

P1 S D D P2 -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways

P1 S P2 D D -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways

P1 P2 D D S -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways

P1 P2 S D D -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways

Total = 16 ways.

Number of ways both the daughters NOT sit near each other = 48-16= 32

WHat is OA?

_________________

To find what you seek in the road of life, the best proverb of all is that which says:

"Leave no stone unturned."

-Edward Bulwer Lytton