Question

Please help, I’m very stuck today.

A debate team consists of five girls and four boys. (Everyone is distinguishable.) How many ways can they stand in line, so that at least two of the girls are standing next to each other?

Answer 1

Answer: 360000

Explanation:

Given

There are 5 girls and 4 boys

Total no of ways in which 5 girls and 4 boys can be arranged is 9!

and no ways in which atleast two girls are standing next to each other is given by

=Total no of arrangements - No of ways in which each girl is separated by a boy

So, no of ways in which each girl is separated by a boy

`=5! * 4!`

Therefore total no of ways in which atleast two girls are standing next to each other

`=9!-5!* 4!`

`=362880-2880`

`=360000`