Three boys and three girls go out for dinner. A shy boy does not want to sit with any girl and a shy girl does not want any boy as a neighbour. How many seating arrangements are possible?
To solve this problem, we can use permutations.
Let's first consider the seating arrangement for the three boys. Since the shy boy does not want to sit with any girl, he has two options for his seat - he can either sit on the leftmost or rightmost seat. The remaining two boys can sit in the other two seats in 2! = 2 ways.
Next, let's consider the seating arrangement for the three girls. Since the shy girl does not want any boy as a neighbor, she also has two options for her seat - either the leftmost or rightmost seat. The remaining two girls can sit in the other two seats in 2! = 2 ways.
So far, we have considered the seating arrangements for the boys and the girls separately. However, since the arrangement of boys and girls is independent of each other, we can multiply the number of arrangements for boys and girls to obtain the total number of seating arrangements.
Therefore, the total number of seating arrangements is 2 * 2 = 4.
Thus, there are four possible seating arrangements.