Question

How many ways are there to seat six boys and eight girls in a row of chairs so that no two boys are seated next to each other?

Short answer

The number of different ways to seat six boys and eight girls in a row of chairs such that no two boys are seated next to each other is \({\rm{20321280}}\)ways.

Step-by-step solution

Assume the seats.

To find the ways to seat six boys and eight girls.So the number of different ways to seat six boys and eight girls in a row of chairs such that no two boys are seated next two each other, first we will arrange eight girls in \(P(8,8) = 8! = 40320\) ways such that between each pair of a girl will allow to seat a boy.

 Arrangements

Now we can have\({\rm{9}}\)positions for six boys, this can be arranged in

\(P(9,6) = 9 \times 8 \times 7 = 504\)

Therefore, the required number of different ways to seat six boys and eight girls in a row of chairs such that no two boys are seated next to each other is \({\rm{20321280}}\) ways.