In how many ways can 4 boys and 4 girls sit around a circle table if all the boys sit together? (Rotations of the same arrangement are still considered the same. Each boy and girl is unique, not interchangeable.)
I do not understand this!
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http://www.jiskha.com/display.cgi?id=1446063633
To understand this problem, let's break it down step by step.
First, we know that all the boys need to sit together. This means that the group of boys can be treated as one entity. So, instead of 4 boys, we now have 1 "group" of boys.
Now, we have 1 group of boys and 4 girls, making a total of 5 entities to be seated around a circular table.
To solve this problem, we use the concept of circular permutations. In a circular permutation, the order of the objects matters, but the starting point of the arrangement does not.
Given 'n' objects, the number of circular permutations can be calculated as (n-1)!
In this case, we have 5 entities to be seated in a circular arrangement, so we apply the formula:
Number of circular permutations = (5-1)! = 4!
To calculate 4!, multiply all the numbers from 4 down to 1:
4! = 4 x 3 x 2 x 1 = 24.
Therefore, there are 24 different ways in which the 4 boys and 4 girls can sit around the table with all the boys sitting together.