Afamily 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?

Answer and Explanation:

We can accommodate the sisters separately in two different ways:

1. Case 1 : One of the sisters is on front seat , i.e. it can be done in two ways. Other members (including the second sister) are arranged in: 2×3! ways

i.e. 12 ways. Therefore total ways for this particular case = 2×12=24  ways

2. Case 2 : Both sister sat by the window seat , it can be achieved in 2 ways. Other members can be accommodated in 2×2×1 = 4 ways.

Therefore total ways for this case= 2×4 = 8.

Total ways in which it can be done = 24+8 =32.