# Question #a6eab

Jun 17, 2016

72 ways

#### Explanation:

Picture this happening one person at a time, filling up from the left side.
There are 6 different people who can sit down first.
Let's assume at first it was a girl. Number of ways = 3
A boy has to sit next to her, there are 3 possible boys to choose from. Number of ways = 3 x 3.
A girl sits down next. There are 2 girls left.
Number of ways = 3 x 3 x 2

Now a boy sits down. There are 2 boys it could be
Number of ways = 3 x 3 x 2 x 2

There is only 1 girl and then 1 boy left to sit, so there is no choice.
Number of ways = 3 x 3 x 2 x 2 x 1 x 1 = 36 ways if a girl sat first.

In the same way if a boy sat first there would be 36 ways for the 6 people to be seated.

Total number of different way = 36 +36 = 72

The same result would be obtained if anyone sat down first.
Number of ways = 6.
However, once the first person is seated there is a condition for the next person and so on.
This leads to the number of ways= 6 x 3 x 2 x 2 x 1 x 1 = 72.