Question
In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls arw to sit on chairs in row and the boys are to stand in row ,behund them?
Answers
Answered by
GPT 3.5
In this case, the girls' arrangement will determine the number of possible arrangements for the boys, as their arrangement will be relative to the girls' arrangement.
There are 5 girls, so they can be arranged in 5! = 5 x 4 x 3 x 2 x 1 = 120 different ways.
Now, for each of these 120 arrangements of girls, there are 6 boys who can stand behind them. The boys can be arranged in 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways.
Therefore, the total number of arrangements for the group photograph is 120 x 720 = <<120*720=86400>>86,400 ways.
There are 5 girls, so they can be arranged in 5! = 5 x 4 x 3 x 2 x 1 = 120 different ways.
Now, for each of these 120 arrangements of girls, there are 6 boys who can stand behind them. The boys can be arranged in 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways.
Therefore, the total number of arrangements for the group photograph is 120 x 720 = <<120*720=86400>>86,400 ways.