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?
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.
To find the number of ways to arrange 6 boys and 5 girls for the group photograph, we need to consider the arrangements of both the boys and the girls separately and then multiply them together.
First, let's find the number of ways to arrange the 5 girls in a row. Since each girl needs to sit on a chair, their arrangement will be in a fixed order. Therefore, the number of ways to arrange the girls is simply the factorial of the number of girls, which is 5!, or 5 factorial.
Next, let's find the number of ways to arrange the 6 boys standing behind the girls. Similar to the girls' arrangement, the boys' arrangement will also be in a fixed order since they are standing in a row. Therefore, the number of ways to arrange the boys is the factorial of the number of boys, which is 6!.
Finally, we can multiply the number of ways to arrange the girls by the number of ways to arrange the boys to get the total number of arrangements. In this case, the total number of arrangements is equal to 5! × 6!.
Hence, there are (5! × 6!) ways to arrange 6 boys and 5 girls for the group photograph.
To determine the number of ways to arrange the boys and girls for the group photograph, we need to follow these steps:
1. Arrange the girls on chairs in a row: There are 5 girls, and they need to be arranged in a row. The number of ways to do this is 5!.
2. Arrange the boys standing behind the girls: There are 6 boys, and they need to stand in a row behind the girls. The number of ways to arrange them is 6!.
3. Multiply the results: Since both the arrangements of girls and boys are independent, we can multiply the results from step 1 and step 2.
So, the total number of ways to arrange the 6 boys and 5 girls for the group photograph is:
5! * 6! = 120 * 720 = 86,400 ways.