In how many ways can Joe, Mary, Steve, and Brenda be seated around a round table?
4! = 4 factorial = 4 * 3 * 2 * 1
To find the number of ways Joe, Mary, Steve, and Brenda can be seated around a round table, we can use the concept of permutations.
Since the table is round, the seating arrangement can be rotated without actually changing the relative positions of the people. Thus, we need to divide the total number of arrangements by the number of rotations to account for this.
Step 1: Find the number of total arrangements.
We have 4 people, so the total number of arrangements is 4!.
Step 2: Find the number of rotations.
Since there are 4 people, there are 4 possible rotations for each arrangement.
Step 3: Divide the total number of arrangements by the number of rotations.
The number of ways the 4 people can be seated around the table is given by:
Total number of arrangements / Number of rotations = 4! / 4
Step 4: Simplify the expression.
4! = 4 x 3 x 2 x 1 = 24
24 / 4 = 6
Therefore, there are 6 different ways Joe, Mary, Steve, and Brenda can be seated around the round table.
To find the number of ways Joe, Mary, Steve, and Brenda can be seated around a round table, we can use the concept of permutations.
Firstly, let's assume that the round table has no distinguishing features, like labels or positions. We want to count the number of ways these four people can be arranged relative to each other.
Step 1: Determine the total number of people (n).
In this case, we have four people: Joe, Mary, Steve, and Brenda. So, n = 4.
Step 2: Find the number of ways to arrange n objects in a line.
The number of ways to arrange n objects in a line is given by n!.
For example, if we had three objects, there would be 3! = 3 x 2 x 1 = 6 ways to arrange them in a line. Similarly, for four objects, there would be 4! = 4 x 3 x 2 x 1 = 24 ways to arrange them in a line.
Step 3: Account for circular arrangements.
Since the people are sitting around a round table, we need to account for the circular nature of the seating arrangement. This means that any arrangement could be rotated to yield the same relative positions.
To adjust for this, we divide the total number of arrangements by the number of rotations possible, which is equal to the number of people (n).
In this case, we have already determined that there are 24 ways to arrange the people in a line. Since there are 4 people, we divide by 4, resulting in 24/4 = 6 arrangements.
Therefore, Joe, Mary, Steve, and Brenda can be seated around the round table in 6 different ways.