permutations

vscid 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?

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

There are two possibilities

a) Parent and a girl on front; others on back seat
b) Both the girls on back separated by a parent or son


P G
_ _ _


a)If a parent is driving; there are 2 ways fill the front seat
Now if a girl is sitting in the front seat she can be selected in 2 ways
Rest of them can be arranged in 3! ways

No of ways 2*2*6 =24

P _
G1 _ G2


b) Parent can be selected in 2 ways
One to accompany in front seats can be selected in 2 ways
One who sitting in the middle can be selected in one way
Girls can be arranged in 2 ways

no of ways = 2*2*2 =8

Total ways = 8+24 =32